Changeset 3d9a64 in git

Timestamp:

Apr 16, 2018, 11:44:16 AM (5 years ago)

Author:

Karim Abou Zeid <karim23697@…>

Branches:

(u'spielwiese', '8e0ad00ce244dfd0756200662572aef8402f13d5')

Children:

c0631ae6149e52d818a36d53440af6c8ccc715f9

Parents:

c1af7fb9ab8e720d1a1fed0afc5d8e134af9d107

Message:

Update fpadim_lib docu

File:

• Singular/LIB/fpaprops.lib (modified) (4 diffs)

Singular/LIB/fpaprops.lib

@@ -18 +18 @@
 
 PROCEDURES:
-  lpNoetherian(<GB>);     check whether A/<LM(GB)> is (left/right) noetherian
+  lpNoetherian(<GB>);     check whether A/<LM(GB)> is (left/right) Noetherian
   lpIsSemiPrime(<GB>);    check whether A/<LM(GB)> is semi prime
   lpIsPrime(<GB>);        check whether A/<LM(GB)> is prime
@@ -33 +33 @@
 "USAGE: lpNoetherian(G); G an ideal in a Letterplace ring
 RETURN: int
-@*      0 not noetherian
-@*      1 left noetherian
-@*      2 right noetherian
-@*      3 noetherian
+@*      0 not Noetherian
+@*      1 left Noetherian
+@*      2 right Noetherian
+@*      3 Noetherian
+@*      4 weak Noetherian (TODO)
 PURPOSE: Check whether the monomial algebra A/<LM(G)> is (left/right) noetherian
 ASSUME: - basering is a Letterplace ring
 @*      - G is a Groebner basis
-NOTE: A/<LM(G)> (left/right) noetherian implies A/<G> (left/right) noetherian
+THEORY: lpNoetherian works with the monomial algebra A/<LM(G)>.
+If it gives an affirmative answer for one of the properties, then it 
+holds for both A/<LM(G)> and A/<G>. However, a negative answer applies 
+only to A/<LM(G)> and not necessarily to A/<G>.
+NOTE: Weak Noetherian means that two-sided ideals in A/<G> satisfy
+the acc (ascending chain condition).
 "
 {
@@ -203 +209 @@
 ASSUME: - basering is a Letterplace ring
       - G is a Groebner basis
+THEORY: lpIsSemiPrime works with the monomial algebra A/<LM(G)>.
+A positive answer holds for both A/<LM(G)> and A/<G>, while 
+a negative answer applies only to A/<LM(G)> and not necessarily to 
+A/<G>.
 "
 {
@@ -304 +314 @@
 ASSUME: - basering is a Letterplace ring
       - G is a Groebner basis
+THEORY: lpIsPrime works with the monomial algebra A/<LM(G)>.
+A positive answer holds for both A/<LM(G)> and A/<G>, while
+a negative answer applies only to A/<LM(G)> and not necessarily to A/<G>.
 "
 {