The local finite basis property and local representability of varieties of associative rings

Belov, A. Ya.

doi:10.1070/im2010v074n01abeh002481

Cited by 18 publications

(5 citation statements)

References 95 publications

(120 reference statements)

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“…The Specht problem was first proved by A.R.Kemer in [20]. Different other proofs can be found in [15]; Positive characteristic case treated in [2]. In particular, the A.Grishin and A.K.-B.…”

Section: Around Specht Problemmentioning

confidence: 99%

On finite dimensionality of homology of subalgebras of vector fields

Feigin¹,

Kanel-Belov²,

Khoroshkin³

2022

Preprint

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Section: Around Specht Problemmentioning

confidence: 99%

On finite dimensionality of homology of subalgebras of vector fields

Feigin¹,

Kanel-Belov²,

Khoroshkin³

2022

Preprint

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“…Then We need a few auxiliary lemmas. The first one is an analogue of the hiking procedure from [21,3].…”

Section: The Group Aut Indmentioning

confidence: 99%

“…The next lemma provides for some translation between the language of polynomials and the group action language. It is similar to the hiking process [3,21].…”

Section: The Group Aut Indmentioning

confidence: 99%

On the augmentation topology of automorphism groups of affine spaces and algebras

Kanel-Belov

Elishev

2018

Int. J. Algebra Comput.

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“…This paper is part of an ongoing project, elaborating [3], [6], to lay a firm foundation for Belov's positive solution for Specht's problem for affine algebras with polynomial identity (PI-algebras) in characteristic p > 0; cf. [3].…”

Section: Introductionmentioning

confidence: 99%

Full quivers of representations of algebras

Belov-Kanel¹,

Rowen²,

Vishne³

2012

Trans. Amer. Math. Soc.

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We introduce the notion of the full quiver of a representation of an algebra, which is a cover of the (classical) quiver, but which captures properties of the representation itself. Gluing of vertices and of arrows enables one to study subtle combinatorial aspects of algebras which are lost in the classical quiver. Full quivers of representations apply especially well to \Zcd\ algebras, which have properties very like those of finite dimensional algebras over fields. By choosing the representation appropriately, one can restrict the gluing to two main types: {\it Frobenius} (along the diagonal) and, more generally {\it proportional} Frobenius gluing (above the diagonal), and our main result is that any representable algebra has a faithful representation described completely by such a full quiver. Further reductions are considered, which bear on the polynomial identities.Comment: 44 p

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The local finite basis property and local representability of varieties of associative rings

Abstract: We prove the local representability and local finite basis property of varieties of associative rings and algebras over an arbitrary associative-commutative Noetherian ring Φ.

Cited by 18 publications

References 95 publications

On finite dimensionality of homology of subalgebras of vector fields

On finite dimensionality of homology of subalgebras of vector fields

On the augmentation topology of automorphism groups of affine spaces and algebras

Full quivers of representations of algebras

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