Loewy Modules with Finite Loewy Invariants and Max Modules with Finite Radical Invariants |
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Authors: | Alberto Facchini Mai Hoang Bien |
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Institution: | 1. Dipartimento di Matematica , Università di Padova , Padova , Italy facchini@math.unipd.it;3. Dipartimento di Matematica , Università di Padova , Padova , Italy |
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Abstract: | Over a commutative ring R, a module is artinian if and only if it is a Loewy module with finite Loewy invariants 5
Facchini , A. ( 1981 ). Loewy and artinian modules over commutative rings . Ann. Mat. Pura Appl. 128 : 359 – 374 .Crossref], Web of Science ®] , Google Scholar]]. In this paper, we show that this is not necesarily true for modules over noncommutative rings R, though every artinian module is always a Loewy module with finite Loewy invariants. We prove that every Loewy module with finite Loewy invariants has a semilocal endomorphism ring, thus generalizing a result proved by Camps and Dicks for artinian modules 3
Camps , R. ,
Dicks , W. ( 1993 ). On semilocal rings . Israel J. Math. 81 : 203 – 211 .Crossref], Web of Science ®] , Google Scholar]]. Finally, we obtain similar results for the dual class of max modules. |
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Keywords: | Endomorphism ring Loewy module Max module Module Semilocal ring |
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