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Operads and varieties of algebras defined by polylinear identities

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dc.contributor.author Tronin S.
dc.date.accessioned 2018-09-18T20:31:35Z
dc.date.available 2018-09-18T20:31:35Z
dc.date.issued 2006
dc.identifier.issn 0037-4466
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/140787
dc.description.abstract We show that varieties of algebras over abstract clones and over the corresponding operads are rationally equivalent. We introduce the class of operads (which we call commutative for definiteness) such that the varieties of algebras over these operads resemble in a sense categories of modules over commutative rings. In particular, the notions of a polylinear mapping and the tensor product of algebras. The categories of modules over commutative rings and the category of convexors are examples of varieties over commutative operads. By analogy with the theory of linear multioperator algebras, we develop a theory of C-linear multioperator algebras; in particular, of algebras, defined by C-polylinear identities (here C is a commutative operad). We introduce and study symmetric C-linear operads. The main result of this article is as follows: A variety of C-linear multioperator algebras is defined by C-polylinear identities if and only if it is rationally equivalent to a variety of algebras over a symmetric C-linear operad. © 2006 Springer Science+Business Media, Inc.
dc.relation.ispartofseries Siberian Mathematical Journal
dc.subject Algebra
dc.subject Identity
dc.subject Operad
dc.subject Rational equivalence
dc.subject Variety
dc.title Operads and varieties of algebras defined by polylinear identities
dc.type Article
dc.relation.ispartofseries-issue 3
dc.relation.ispartofseries-volume 47
dc.collection Публикации сотрудников КФУ
dc.relation.startpage 555
dc.source.id SCOPUS00374466-2006-47-3-SID33744754361


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  • Публикации сотрудников КФУ Scopus [24551]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

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