TY - JOUR

T1 - On a Shirshov basis of relatively free algebras of complexity n

AU - Belov, A.

N1 - Belov, Aleksei Yakovlevich. "On a Shirshov basis of relatively free algebras of complexity n." Matematicheskii Sbornik 177.3 (1988): 373-384.

PY - 1988

Y1 - 1988

N2 - A Shirshov basis is a set of elements of an algebra AA over which AA has bounded height in the sense of Shirshov.
A description is given of Shirshov bases consisting of words for associative or alternative relatively free algebras over an arbitrary commutative associative ring ΦΦ with unity. It is proved that the set of monomials of degree at most m2m2 is a Shirshov basis in a Jordan PI-algebra of degree mm. It is shown that under certain conditions on var(B)var(B) (satisfied by alternative and Jordan PI-algebras), if each factor of BB with nilpotent projections of all elements of MM is nilpotent, then MM is a Shirshov basis of BB if MM generates BB as an algebra.
Bibliography: 12 titles.

AB - A Shirshov basis is a set of elements of an algebra AA over which AA has bounded height in the sense of Shirshov.
A description is given of Shirshov bases consisting of words for associative or alternative relatively free algebras over an arbitrary commutative associative ring ΦΦ with unity. It is proved that the set of monomials of degree at most m2m2 is a Shirshov basis in a Jordan PI-algebra of degree mm. It is shown that under certain conditions on var(B)var(B) (satisfied by alternative and Jordan PI-algebras), if each factor of BB with nilpotent projections of all elements of MM is nilpotent, then MM is a Shirshov basis of BB if MM generates BB as an algebra.
Bibliography: 12 titles.

UR - http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sm&paperid=1708&option_lang=eng

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VL - 135

SP - 373

EP - 384

JO - Matematicheskii Sbornik

JF - Matematicheskii Sbornik

IS - 3

ER -