Systems of generators of t-ideals of finitely generated free algebras

Markov, V. T.

doi:10.1007/bf01673503

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Finitely Presented Relatively Free Algebras1

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Cited by 12 publications

(9 citation statements)

References 4 publications

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“…Theorem 4.21 (V. T. Markov,251]). Let V and V 0 be two varieties of associative algebras with units.…”

Section: Finitely Presented Relatively Free Algebrasmentioning

confidence: 99%

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Algorithmic Problems in Varieties

Kharlampovich

Sapir

1995

Int. J. Algebra Comput.

151

120

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“…Theorem 4.21 (V. T. Markov,251]). Let V and V 0 be two varieties of associative algebras with units.…”

Section: Finitely Presented Relatively Free Algebrasmentioning

confidence: 99%

“…Theorem 4.22 (V. T.Markov,251]). For any n 2 the relatively free algebra in M n with more than one generator is not nitely presented in the variety M n+1 , furthermore it is not absolutely nitely presented.…”

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confidence: 99%

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Algorithmic Problems in Varieties

Kharlampovich

Sapir

1995

Int. J. Algebra Comput.

151

120

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“…Let p be the characteristic of a field F . Denote by M the variety of F -algebras given by two identities [x p , y] = 0, (6) and…”

Section: Examplementioning

confidence: 99%

“…Algebras A(F ), A(F ) ⋆ , B(F, G, σ) from Theorem 2 are non-Engel (see Proposition 2). Therefore, they do not satisfy Identity (6), that is p-Engel condition, and can not belong to M.…”

Section: Examplementioning

confidence: 99%

Almost Lie nilpotent varieties of associative algebras

Finogenova

2011

Preprint

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We consider associative algebras over a field. An algebra variety is said to be Lie nilpotent if it satisfies a polynomial identity of the kind [x 1 , x 2 , . . . , x n ] = 0 where [ x 1 , x 2 ] = x 1 x 2 − x 2 x 1 and [x 1 , x 2 By Zorn's Lemma every non-Lie nilpotent variety contains a minimal such variety, called almost Lie nilpotent, as a subvariety. A description of almost Lie nilpotent varieties for algebras over a field of characteristic 0 was made up by Yu.Mal'cev. We find a list of non-prime almost Lie nilpotent varieties of algebras over a field of positive characteristic.

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Locally Noetherian and locally representable varieties of alternative algebras

Pchelintsev¹

1989

Sib Math J

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Systems of generators of t-ideals of finitely generated free algebras

Cited by 12 publications

References 4 publications

Algorithmic Problems in Varieties

Algorithmic Problems in Varieties

Almost Lie nilpotent varieties of associative algebras

Locally Noetherian and locally representable varieties of alternative algebras

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