The Golod property of powers of the maximal ideal of a local ring
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DOI: 10.1007/s00013-018-1152-6
Abstract: We identify minimal cases in which a power $$\mathfrak {m}^i\not =0$$mi≠0 of the maximal ideal of a local ring R is not Golod, i.e. the quotient ring $$R/\mathfrak {m}^i$$R/mi is not Golod. Complementary to a… read more here.
Keywords: ideal local; maximal ideal; mathfrak; ring golod ... See more keywords
Depth of ideals of C(X)
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DOI: 10.1016/j.jalgebra.2019.03.018
Abstract: Abstract We show that every regular sequence in C ( X ) has length ≤1. This shows that depth ( C ( X ) ) ≤ 1 . We also show that the depth of… read more here.
Keywords: factor rings; depth maximal; depth ideals; depth ... See more keywords
Polarizations and hook partitions
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DOI: 10.1016/j.jpaa.2022.107056
Abstract: In this paper, we relate combinatorial conditions for polarizations of powers of the graded maximal ideal with rank conditions on submodules generated by collections of Young tableaux. We apply discrete Morse theory to the hypersimplex… read more here.
Keywords: graded maximal; maximal ideal; polarizations hook; hook partitions ... See more keywords
POWERS OF THE MAXIMAL IDEAL AND VANISHING OF (CO)HOMOLOGY
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DOI: 10.1017/s0017089519000466
Abstract: Abstract We prove that each positive power of the maximal ideal of a commutative Noetherian local ring is Tor-rigid and strongly rigid. This gives new characterizations of regularity and, in particular, shows that such ideals… read more here.
Keywords: powers maximal; ideal vanishing; vanishing homology; maximal ideal ... See more keywords