Monomial regular sequences
نویسندگان
چکیده
منابع مشابه
Almost Regular Sequences and the Monomial Conjecture
This conjecture has assumed a central role since it has a very simple statement and it implies several other important conjectures, notably the Canonical Element Conjecture, for rings of positive or mixed characteristic. In fact, when this conjecture was first announced, it had numerous further consequences, some of which, such as the New Intersection Conjecture, were proved later by different ...
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Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.
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In this note we exhibit a condition under which a sequence of elements a19 , an in a commutative noetherian local ring A form an Asequence, and derive a number of corollaries. Recall that if M is an A-module, then a19 , an is an M-sequence if 1) ai+1 is a nonzerodivisor on M/(a19 9a1)M for i = 0, 9n — 1,. and 2) M Φ (al9 . . . , α n ) M . If a19 , an is an A-sequence and / is the ideal generate...
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A set of n homogeneous polynomials in n variables is a regular sequence if the associated polynomial system has only the obvious solution (0, 0, . . . , 0). Denote by pk(n) the power sum symmetric polynomial in n variables x k 1 +x 2 + · · ·+xk n . The interpretation of the q-analogue of the binomial coefficient as Hilbert function leads us to discover that n consecutive power sums in n variabl...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2010
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-10-10244-5