Almost perfect commutative rings |
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Authors: | László Fuchs Luigi Salce |
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Affiliation: | 1. Department of Mathematics, Tulane University, New Orleans, LA 70118, USA;2. Dipartimento di Matematica “Tullio Levi-Civita”, Università di Padova, Padova, Italy |
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Abstract: | Almost perfect commutative rings R are introduced (as an analogue of Bazzoni and Salce's almost perfect domains) for rings with divisors of zero: they are defined as orders in commutative perfect rings such that the factor rings are perfect rings (in the sense of Bass) for all non-zero-divisors. It is shown that an almost perfect ring is an extension of a T-nilpotent ideal by a subdirect product of a finite number of almost perfect domains. Noetherian almost perfect rings are exactly the one-dimensional Cohen–Macaulay rings. Several characterizations of almost perfect domains carry over practically without change to almost perfect rings. Examples of almost perfect rings with zero-divisors are abundant. |
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Keywords: | Primary 13C13 secondary 13C11 |
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