closing some issues towards v2.0 release

doc/LocalNR.bib

@@ -0,0 +1,45 @@
+@article {MR2799412,
+    AUTHOR = {Sysak, Yaroslav P.},
+     TITLE = {Products of groups and local nearrings},
+   JOURNAL = {Note Mat.},
+  FJOURNAL = {Note di Matematica},
+    VOLUME = {28},
+      YEAR = {2008},
+     PAGES = {181--216},
+      ISSN = {1123-2536,1590-0932},
+   MRCLASS = {16Y30 (20D40)},
+  MRNUMBER = {2799412},
+}
+
+@article {MR4943879,
+    AUTHOR = {Raievska, Iryna and Raievska, Maryna},
+     TITLE = {Local nearrings, their structure, and the gap system},
+   JOURNAL = {Ukrainian Math. J.},
+  FJOURNAL = {Ukrainian Mathematical Journal},
+    VOLUME = {76},
+      YEAR = {2025},
+    NUMBER = {11},
+     PAGES = {1831--1848},
+      ISSN = {0041-5995,1573-9376},
+   MRCLASS = {16Y30 (20M10)},
+  MRNUMBER = {4943879},
+MRREVIEWER = {Figen\ Tak\i l{} Mutlu},
+       DOI = {10.1007/s11253-025-02426-y},
+       URL = {https://doi.org/10.1007/s11253-025-02426-y},
+}
+
+@article {MR230773,
+    AUTHOR = {Maxson, Carlton J.},
+     TITLE = {On local near-rings},
+   JOURNAL = {Math. Z.},
+  FJOURNAL = {Mathematische Zeitschrift},
+    VOLUME = {106},
+      YEAR = {1968},
+     PAGES = {197--205},
+      ISSN = {0025-5874,1432-1823},
+   MRCLASS = {16.96},
+  MRNUMBER = {230773},
+MRREVIEWER = {L.\ J.\ Ratliff, Jr.},
+       DOI = {10.1007/BF01110133},
+       URL = {https://doi.org/10.1007/BF01110133},
+}

lib/lib_local.gd

@@ -2,11 +2,11 @@
 ##
 ##                            LocalNR - a GAP package of local nearrings
 ##
-##  Copyright 2019,                Yaroslav Sysak with contributions by
+##  Copyright 2026,                Yaroslav Sysak with contributions by
 ##                                      Iryna Raievska, Maryna Raievska
 ##                  
-##  Institute of Mathematics of National Academy of Sciences of Ukraine
-##
+##  Institute of Mathematics of National Academy of Sciences of Ukraine,
+##  Kyiv, Ukraine
 #############################################################################
 
 
@@ -15,8 +15,9 @@
 #! @Chapter Local nearrings
 ##
 ###################################
-
-#! A set $R$ with two binary operations $+$ and $\cdot$ is called 
+#! 
+#!
+#! A set $R$ with two binary operations $+$ and $\cdot$ is called
 #! a <Emph>(left) nearring</Emph> if the following statements hold:
 #! 
 #! <Enum>
@@ -31,26 +32,44 @@
 #! </Item>
 #! </Enum>
 #! 
-#! If $R$ is a nearring, then the group $R^+$  is called 
-#! the <Emph>additive group</Emph> of $R$. 
-#! If in addition $0\cdot x=0$, then the nearring $R$ is 
-#! called <Emph>zero-symmetric</Emph>, and if the 
-#! semigroup $(R,\cdot)$ is a monoid, i.e. it has 
-#! an identity element $i$, then  $R$ is 
-#! a <Emph>nearring with identity</Emph> $i$. In the 
+#! If $R$ is a nearring, then the group $R^+$  is called
+#! the <Emph>additive group</Emph> of $R$.
+#! If in addition $0\cdot x=0$, then the nearring $R$ is
+#! called <Emph>zero-symmetric</Emph>, and if the
+#! semigroup $(R,\cdot)$ is a monoid, i.e. it has
+#! an identity element $i$, then  $R$ is
+#! a <Emph>nearring with identity</Emph> $i$. In the
 #! latter case the group $R^*$ of all invertible elements of  
-#! the monoid $(R,\cdot)$ is called the <Emph>multiplicative group</Emph> of $R$.   
+#! the monoid $(R,\cdot)$ is called the <Emph>multiplicative group</Emph> of $R$.  
 #! 
-#! A nearring $R$ with identity is said to be 
-#! <Emph>local</Emph> if the set $L=R\setminus R^*$ of all 
-#! non-invertible elements of $R$ is a subgroup of $R^+$. 
+#! The concepts of a subnearring and a nearring homomorphism are defined
+#! by the same way as for rings. In particular,
+#! if $\lambda$ is a nearring homomorphism of $(R,+, \cdot)$,
+#! then its kernel $Ker \lambda$ is a subnearring of $(R,+, \cdot)$
+#! whose additive subgroup is normal in $R^+$.
 #! 
-#! It is clear that if $L$ is an 
-#! ideal of $R$, then the factor nearring $R/L$ is a <Emph>nearfield</Emph>. For example, 
-#! every local ring $R$ is a zero-symmetric local nearring whose 
-#! subgroup $L$ coincides 
-#! with the Jacobson radical of $R$.
-
+#! A subnearring $I$ of $(R,+, \cdot)$ is an ideal
+#! of $(R,+, \cdot)$ if $I = Ker \lambda$  for some $\lambda$.
+#! 
+#! It can simply be verified that $I$ is an ideal of $R$
+#! if and only if its additive group $I^+$ is a normal subgroup
+#! of $R^+$ and for any elements $r$, $s\in R$ and $a\in I$
+#! the inclusions $ra\in I$ and
+#! $(r + a)s − rs\in I$ hold.
+#! Main results accumulated for local nearrings
+#! can be found in the surveys
+#!  <Cite Key="MR2799412"/> and <Cite Key="MR4943879"/>. 
+#!
+#! A nearring $R$ with identity is said to be
+#! <Emph>local</Emph> if the set $L=R\setminus R^*$ of all
+#! non-invertible elements of $R$ is a subgroup of $R^+$.
+#! 
+#! It is clear that if $L$ is an
+#! ideal of $R$, then the factor nearring $R/L$ is a <Emph>nearfield</Emph>. For example,
+#! every local ring $R$ is a zero-symmetric local nearring whose
+#! subgroup $L$ coincides
+#! with the Jacobson radical of $R$. Reference: 
+#!  <Cite Key="MR230773"/>. 
 ###################################
 ##
 #! @Section The local nearrings library
@@ -66,10 +85,10 @@
 #! @Returns a list
 #! @Arguments n
 #! @Label 
-DeclareGlobalFunction( "TheAdditiveGroupsOfLibraryOfLNRsOfOrder");
+DeclareGlobalFunction( "AdditiveGroupsOfLibraryOfLNRsOfOrder");
 
 #! @BeginExample
-#! gap> List(TheAdditiveGroupsOfLibraryOfLNRsOfOrder(81),IdGroup);
+#! gap> List(AdditiveGroupsOfLibraryOfLNRsOfOrder(81),IdGroup);
 #! [ [ 81, 1 ], [ 81, 2 ], [ 81, 3 ], [ 81, 5 ], [ 81, 6 ], [ 81, 11 ], 
 #!   [ 81, 12 ], [ 81, 13 ], [ 81, 15 ] ]
 #! @EndExample
@@ -83,15 +102,15 @@ DeclareGlobalFunction( "TheAdditiveGroupsOfLibraryOfLNRsOfOrder");
 #! @Returns a list
 #! @Arguments G
 #! @Label 
-DeclareGlobalFunction( "TheLibraryOfLNRsOnGroup");
+DeclareGlobalFunction( "LibraryOfLNRsOnGroup");
 
 #! The local nearrings are sorted by their multiplicative groups.
 
 
 #! @BeginExample
 #! gap> G:=SmallGroup(81,2);
 #! <pc group of size 81 with 4 generators>
-#! gap> TheLibraryOfLNRsOnGroup(G);
+#! gap> LibraryOfLNRsOnGroup(G);
 #! [ "AllLocalNearRings(81,2,54,3)", "AllLocalNearRings(81,2,54,6)", 
 #!   "AllLocalNearRings(81,2,54,9)", "AllLocalNearRings(81,2,54,10)", 
 #!   "AllLocalNearRings(81,2,54,11)", "AllLocalNearRings(81,2,54,15)", 
@@ -136,6 +155,24 @@ DeclareOperation( "AllLocalNearRings", [ IsInt, IsInt, IsInt, IsInt ]);
 
 ###################################
 
+#! @Description
+#! The arguments are $k$, $l$, $m$, $n$.
+#! The output are number of all local nearrings from <C>Library</C> without 
+#! check. The arguments $k$, $l$, $m$, $n$ are as above.
+#! @Returns a number
+#! @Arguments k,l,m,n
+#! @Label
+DeclareOperation( "NumberLocalNearRings", [ IsInt, IsInt, IsInt, IsInt ]);
+
+#! @BeginExample
+#! gap> NumberLocalNearRings(81,15,54,8);
+#! 10
+#! @EndExample
+
+DeclareSynonym("NrLocalNearRings", NumberLocalNearRings);
+
+###################################
+
 #! @Description
 #! The argument is a group $G$. 
 #! The output is <C>true</C> if in <C>Library</C> there exists a local nearring 

lib/lib_local.gi

@@ -12,9 +12,12 @@ InstallMethod( LocalNearRing,
 
       h := DirectoriesPackageLibrary( "LocalNR", Concatenation( "Endom/", String( k ) ) );
       if IsEmpty( h ) then
-        return false;
+        Error("The library of local nearrings of order ", k, " is not available");
       else
         dio := Filename( h, Concatenation( "Endom", String( k ), "_", String( l ), "-", String( m ), "_", String( n ), ".txt" ) );
+        if dio = fail then
+          Error("The library of local nearrings with the additive group [", k, ",", l, "] and multiplicative group [", m, ",", n, "] is not available");
+        fi;
         G := SmallGroup( k, l );
         P1 := ReadAsFunction( dio )();
         P := P1[w];
@@ -59,9 +62,12 @@ InstallMethod( AllLocalNearRings,
 
       h := DirectoriesPackageLibrary( "LocalNR", Concatenation( "Endom/", String( k ) ) );
       if IsEmpty( h ) then
-        return false;
+        Error("The library of local nearrings of order ", k, " is not available");
       else
         w := Filename( h, Concatenation( "Endom", String( k ), "_", String( l ), "-", String( m ), "_", String( n ), ".txt" ) );
+        if w = fail then
+          Error("The library of local nearrings with the additive group [", k, ",", l, "] and multiplicative group [", m, ",", n, "] is not available");
+        fi;
         G := SmallGroup( k, l );
         P1 := ReadAsFunction( w )();
         H := [];
@@ -118,13 +124,36 @@ InstallMethod( AllLocalNearRings,
 ##
 ############################################################################
 ##
-# TheAdditiveGroupsOfLibraryOfLNRsOfOrder
-InstallGlobalFunction(TheAdditiveGroupsOfLibraryOfLNRsOfOrder, function(n)
+# NumberLocalNearRings(<k,l,m,n>)
+InstallMethod( NumberLocalNearRings,
+    "Number of all local nearrings",
+    [ IsInt, IsInt, IsInt, IsInt ],
+    function( k, l, m, n )
+      local w, T, h, s;
+
+      h := DirectoriesPackageLibrary( "LocalNR", Concatenation( "Endom/", String( k ) ) );
+      if IsEmpty( h ) then
+        Error("The library of local nearrings of order ", k, " is not available");
+      else
+        w := Filename( h, Concatenation( "Endom", String( k ), "_", String( l ), "-", String( m ), "_", String( n ), ".txt" ) );
+        if w = fail then
+          Error("The library of local nearrings with the additive group [", k, ",", l, "] and multiplicative group [", m, ",", n, "] is not available");
+        fi;
+        T := ReadAsFunction( w )();
+        s := Size( T );
+        return s;
+       fi;
+     end );
+##
+############################################################################
+##
+# AdditiveGroupsOfLibraryOfLNRsOfOrder
+InstallGlobalFunction(AdditiveGroupsOfLibraryOfLNRsOfOrder, function(n)
   local t, cont, i, h, j, f, g, r, us;
 
   t := DirectoriesPackageLibrary( "LocalNR", Concatenation( "Endom/", String( n ) ) );
   if IsEmpty( t ) then
-    Error( "the order must be PrimePowerInt and 3<n and n<1331 (except orders 128, 256, 512, 625, 729, 1024)" );
+    Error("The library of local nearrings of order ", n, " is not available");
   else
     cont := DirectoryContents( t[1] );
     Size( cont );
@@ -162,12 +191,12 @@ InstallGlobalFunction(IsAdditiveGroupOfLibraryOfLNRs, function(G)
   s := Size( G );
   t := DirectoriesPackageLibrary( "LocalNR", Concatenation( "Endom/", String( s ) ) );
   if IsEmpty( t ) then
-    Error( "false" );
+    Error("The library of local nearrings of order ", s, " is not available");
   else
     cont := DirectoryContents( t[1] );
     Size( cont );
     for i in cont do
-      RemoveCharacters( i, "Endom\.txt\.gz" );
+      RemoveCharacters( i, "Endom.txt.gz" );
     od;
     h := [];
     for j in cont do
@@ -195,20 +224,20 @@ end );
 ##
 ############################################################################
 ##
-# TheLibraryOfLNRsOnGroup
-InstallGlobalFunction(TheLibraryOfLNRsOnGroup, function(G)
+# LibraryOfLNRsOnGroup
+InstallGlobalFunction(LibraryOfLNRsOnGroup, function(G)
 
   local s, t, cont, i, h, j, f, hj, g, r, ee, ww, b, w;
 
   s := Size( G );
   t := DirectoriesPackageLibrary( "LocalNR", Concatenation( "Endom/", String( s ) ) );
   if IsEmpty( t ) then
-    Error( "false" );
+    Error("The library of local nearrings of order ", s, " is not available");
   else
     cont := DirectoryContents( t[1] );
     Size( cont );
     for i in cont do
-      RemoveCharacters( i, "Endom\.txt\.gz" );
+      RemoveCharacters( i, "Endom.txt.gz" );
     od;
     h := [];
     for j in cont do

lib/local.gd

@@ -2,11 +2,11 @@
 ##
 ##                            LocalNR - a GAP package of local nearrings
 ##
-##  Copyright 2019,                Yaroslav Sysak with contributions by
+##  Copyright 2026,                Yaroslav Sysak with contributions by
 ##                                      Iryna Raievska, Maryna Raievska
 ##         
-##  Institute of Mathematics of National Academy of Sciences of Ukraine
-##
+##  Institute of Mathematics of National Academy of Sciences of Ukraine,
+##  Kyiv, Ukraine
 #############################################################################
 
 ###################################
@@ -47,6 +47,8 @@ DeclareProperty( "IsMinimalNonAbelianGroup", IsGroup );
 #! false
 #! @EndExample
 
+DeclareSynonym( "IsMillerMorenoGroup", IsMinimalNonAbelianGroup );
+
 ###################################
 
 #! @Description
@@ -119,9 +121,9 @@ DeclareProperty( "IsEndoCyclicGroup", IsGroup );
 
 #! @Description
 #! The argument is a nearring $R$.
-#! The output is <C>true</C> if $R$ is a nearring with identity,
-#! otherwise the output is <C>Error, no units exist</C>.
-#! @Returns a set
+#! The output is a list of units if $R$ is a nearring with identity,
+#! otherwise the output is an empty list.
+#! @Returns a list
 #! @Arguments  R
 #! @Label 
 DeclareAttribute( "UnitsOfNearRing", IsNearRing  );
@@ -137,6 +139,11 @@ DeclareAttribute( "UnitsOfNearRing", IsNearRing  );
 #! gap> Un:=NearRingUnits(N);;
 #! gap> U=Un;
 #! true
+#! gap> L:=LibraryNearRing(SmallGroup(6,1),3);
+#! #I  using isomorphic copy of the group
+#! LibraryNearRing(6/2, 3)
+#! gap> UnitsOfNearRing(L);
+#! [  ]
 #! @EndExample
 
 ###################################

lib/local.gi

@@ -67,10 +67,10 @@ InstallMethod( IsEndoCyclicGroup,
       h := [];
       for i in [1..t] do
         if Size( F[i][2] ) = Size( G ) then
-          Add( h, F[i][2] );
+          return true;
         fi;
       od;
-      return Size( h ) > 0;
+      return false;
     end );
 
 ##
@@ -84,7 +84,7 @@ InstallMethod( UnitsOfNearRing,
       local A, G, one, x;
 
       if not IsNearRingWithIdentity( R ) then
-        return [];
+         return [];
       else
         G := GroupReduct( R );
         A := AutomorphismGroup( G );