Which series are Hilbert series of graded modules over standard multigraded polynomial rings?
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DOI: 10.1002/mana.201800436
Abstract: Consider a polynomial ring R with the Zn‐grading where the degree of each variable is a standard basis vector. In other words, R is the homogeneous coordinate ring of a product of n projective spaces.… read more here.
Keywords: hilbert series; finitely generated; series finitely; series hilbert ... See more keywords
On finitely generated modules over quasi-Euclidean rings
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DOI: 10.1007/s00013-016-1009-9
Abstract: Let R be a unital commutative ring, and let M be an R-module that is generated by k elements but not less. Let $$\text {E}_n(R)$$En(R) be the subgroup of $$\text {GL}_n(R)$$GLn(R) generated by the elementary… read more here.
Keywords: generated modules; euclidean rings; finitely generated; text ... See more keywords
On Finite Generability of Clones of Finite Posets
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DOI: 10.1007/s11083-019-09486-3
Abstract: In the first part of this paper we present a new family of finite bounded posets whose clones of monotone operations are not finitely generated. The proofs of these results are analogues of those in… read more here.
Keywords: finitely generated; ascending idempotent; finite generability; finite posets ... See more keywords
On Finitely Generated Module Whose First Nonzero Fitting Ideal is Prime
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DOI: 10.1007/s41980-019-00351-y
Abstract: Let R be a commutative ring and M be a finitely generated R -module. Let I( M ) be the first nonzero Fitting ideal of M . The main result of this paper is to… read more here.
Keywords: nonzero fitting; first nonzero; finitely generated; generated module ... See more keywords
On prime rings whose central closure is finitely generated
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DOI: 10.1016/j.jalgebra.2017.06.021
Abstract: Abstract The purpose of the paper is to study prime rings R such that the central closure RC is a simple ring with 1 and it is finitely generated over R by elements of the… read more here.
Keywords: prime rings; closure; finitely generated; whose central ... See more keywords
Puiseux monoids and transfer homomorphisms
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DOI: 10.1016/j.jalgebra.2018.08.026
Abstract: There are several families of atomic monoids whose arithmetical invariants have received a great deal of attention during the last two decades. The factorization theory of finitely generated monoids, strongly primary monoids, Krull monoids, and… read more here.
Keywords: finitely generated; monoids transfer; puiseux monoids; puiseux ... See more keywords
Corrigendum to “Effective subgroup separability of finitely generated nilpotent groups” [J. Algebra 506 (2018) 489–508]
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DOI: 10.1016/j.jalgebra.2018.12.025
Abstract: Abstract The purpose of this short note is to provide a correction to the second statement of [1, Theorem 1.1] . read more here.
Keywords: finitely generated; subgroup separability; generated nilpotent; separability finitely ... See more keywords
On accessibility for pro-p groups
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DOI: 10.1016/j.jalgebra.2019.01.022
Abstract: We define the notion of accessibility for a pro-$p$ group. We prove that finitely generated pro-$p$ groups are accessible given a bound on the size of their finite subgroups. We then construct a finitely generated… read more here.
Keywords: finitely generated; group; pro groups; accessibility pro ... See more keywords
On elasticities of locally finitely generated monoids
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DOI: 10.1016/j.jalgebra.2019.05.031
Abstract: Abstract Let H be a commutative and cancellative monoid. The elasticity ρ ( a ) of a non-unit a ∈ H is the supremum of m / n over all m , n for which… read more here.
Keywords: generated monoids; locally finitely; elasticities locally; finitely generated ... See more keywords
Nil restricted Lie algebras of oscillating intermediate growth
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DOI: 10.1016/j.jalgebra.2021.09.003
Abstract: The Grigorchuk and Gupta-Sidki groups are natural examples of self-similar finitely generated periodic groups. The author constructed their analogue in case of restricted Lie algebras of characteristic 2, Shestakov and Zelmanov extended this construction to… read more here.
Keywords: nil restricted; finitely generated; lie algebras; restricted lie ... See more keywords
Generalizations of projectivity and supplements revisited for superfluous ideals
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DOI: 10.1080/00927872.2018.1468897
Abstract: Abstract We (re)introduce four ideal-related generalizations of classic module-theoretic notions: the ideal-superfluity, projective ideal-covers, the ideal-projectivity, and ideal-supplements. For a superfluous ideal I, the main theorem asserts the equivalence between the conditions: “I-supplements are direct… read more here.
Keywords: projectivity supplements; generalizations projectivity; ideal; finitely generated ... See more keywords