7,226 research outputs found
Homological finiteness properties of monoids, their ideals and maximal subgroups
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
A dichotomy result for prime algebras of Gelfand-Kirillov dimension two
Let be an uncountable field. We show that a finitely generated prime
Goldie -algebra of quadratic growth is either primitive or satisfies a
polynomial identity, answering a question of Small in the affirmative.Comment: 10 page
Identities of finitely generated graded algebras with involution
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
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
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