7,226 research outputs found

    A dichotomy result for prime algebras of Gelfand-Kirillov dimension two

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    Let kk be an uncountable field. We show that a finitely generated prime Goldie kk-algebra of quadratic growth is either primitive or satisfies a polynomial identity, answering a question of Small in the affirmative.Comment: 10 page

    Homological finiteness properties of monoids, their ideals and maximal subgroups

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    We consider the general question of how the homological finiteness property left-FPn holding in a monoid influences, and conversely depends on, the property holding in the substructures of that monoid. In particular we show that left-FPn is inherited by the maximal subgroups in a completely simple minimal ideal, in the case that the minimal ideal has finitely many left ideals. For completely simple semigroups we prove the converse, and as a corollary show that a completely simple semigroup is of type left- and right-FPn if and only if it has finitely many left and right ideals and all of its maximal subgroups are of type FPn. Also, given an ideal of a monoid, we show that if the ideal has a two-sided identity element then the containing monoid is of type left-FPn if and only if the ideal is of type left-FPn.Comment: 25 page

    Identities of finitely generated graded algebras with involution

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    We consider associative algebras with involution graded by a finite abelian group G over a field of characteristic zero. Suppose that the involution is compatible with the grading. We represent conditions permitting PI-representability of such algebras. Particularly, it is proved that a finitely generated (Z/qZ)-graded associative PI-algebra with involution satisfies exactly the same graded identities with involution as some finite dimensional (Z/qZ)-graded algebra with involution for any prime q or q = 4. This is an analogue of the theorem of A.Kemer for ordinary identities, and an extension of the result of the author for identities with involution. The similar results were proved also recentely for graded identities

    Cohomological properties of non-standard multigraded modules

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    In this paper we study some cohomological properties of non-standard multigraded modules and Veronese transforms of them. Among others numerical characters, we study the generalized depth of a module and we see that it is invariant by taking a Veronese transform. We prove some vanishing theorems for the local cohomology modules of a multigraded module; as a corollary of these results we get that the depth of a Veronese module is asymptotically constant

    On a theory of the bb-function in positive characteristic

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    We present a theory of the bb-function (or Bernstein-Sato polynomial) in positive characteristic. Let ff be a non-constant polynomial with coefficients in a perfect field kk of characteristic p>0.p>0. Its bb-function bfb_f is defined to be an ideal of the algebra of continuous kk-valued functions on Zp.\mathbb{Z}_p. The zero-locus of the bb-function is thus naturally interpreted as a subset of Zp,\mathbb{Z}_p, which we call the set of roots of bf.b_f. We prove that bfb_f has finitely many roots and that they are negative rational numbers. Our construction builds on an earlier work of Musta\c{t}\u{a} and is in terms of DD-modules, where DD is the ring of Grothendieck differential operators. We use the Frobenius to obtain finiteness properties of bfb_f and relate it to the test ideals of f.f.Comment: Final versio
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