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Abstract
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We introduce a new class of commutative nonnoetherian rings, called
-subperfect rings,
generalizing the almost perfect rings that have been studied recently by Fuchs and Salce. For an
integer
, the ring
is said to be
-subperfect if every maximal
regular sequence in
has
length
and the total
ring of quotients of
for any ideal
generated by a regular sequence is a perfect ring in the sense of Bass.
We define an extended Cohen–Macaulay ring as a commutative ring
that has noetherian prime spectrum and each localization
at a maximal
ideal
is
-subperfect.
In the noetherian case, these are precisely the classical Cohen–Macaulay
rings. Several relevant properties are proved reminiscent of those shared by
Cohen–Macaulay rings.
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Keywords
Perfect, subperfect, $n$-subperfect rings, regular
sequence, unmixed, Cohen–Macaulay rings
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Mathematical Subject Classification 2010
Primary: 13F99, 13H10
Secondary: 13C13
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Milestones
Received: 6 January 2018
Revised: 18 April 2019
Accepted: 28 April 2019
Published: 21 December 2019
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