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On rings whose modules have nonzero homomorphisms to nonzero submodules
Tolooei, Y.
Vedadi, M. R.

Data: 2013
Resum: 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.
Drets: Tots els drets reservats
Llengua: Anglès
Document: article ; recerca ; publishedVersion
Matèria: CPF rings ; Max ring ; Regular ring ; Retractable ; Semi-Artinian
Publicat a: Publicacions matemàtiques, Vol. 57, Núm. 1 (2013) , p. 107-122, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_57113_04

16 p, 349.9 KB

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