| Date: |
2013 |
| Abstract: |
We carry out a study of rings R for which HomR (M;N) 6= 0 for all nonzero N ≤ MR. Such rings are called retractable. For a retractable ring, Artinian condition and having Krull dimension are equivalent. Furthermore, a right Artinian ring in which prime ideals commute is precisely a right Noetherian retractable ring. Retractable rings are characterized in several ways. They form a class of rings that properly lies between the class of pseudo-Frobenius rings, and the class of max divisible rings for which the converse of Schur's lemma holds. For several types of rings, including commutative rings, retractability is equivalent to semi-Artinian condition. We show that a Kothe ring R is an Artinian principal ideal ring if and only if it is a certain retractable ring, and determine when R is retractable. |
| Rights: |
Tots els drets reservats.  |
| Language: |
Anglès |
| Document: |
Article ; recerca ; Versió publicada |
| Subject: |
CPF rings ;
Max ring ;
Regular ring ;
Retractable ;
Semi-Artinian |
| Published in: |
Publicacions matemàtiques, Vol. 57, Núm. 1 (2013) , p. 107-122, ISSN 2014-4350 |
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