Nearly Finite-Dimensional Jordan Algebras

V. N. Zhelyabin, A. S. Panasenko

Результат исследования: Научные публикации в периодических изданияхстатья

Аннотация

Nearly finite-dimensional Jordan algebras are examined. Analogs of known results are considered. Namely, it is proved that such algebras are prime and nondegenerate. It is shown that the property of being nearly finite-dimensional is preserved in passing from an alternative algebra to an adjoint Jordan algebra. A similar result is established for associative nearly finite-dimensional algebras with involution. It is stated that a nearly finite-dimensional Jordan PI-algebra with unity either is a finite module over a nearly finite-dimensional center or is a central order in an algebra of a nondegenerate symmetric bilinear form. Also the following result holds: if a locally nilpotent ideal has finite codimension in a Jordan algebra with the ascending chain condition on ideals, then that algebra is finite-dimensional. In addition, E. Formanek’s result in [Comm. Alg., 1, No. 1, 79-86 (1974)], which says that associative prime PI-rings with unity are embedded in a free module of finite rank over its center, is generalized to Albert rings.

Язык оригиналаанглийский
Страницы (с-по)336-352
Число страниц17
ЖурналAlgebra and Logic
Том57
Номер выпуска5
DOI
СостояниеОпубликовано - 1 ноя 2018

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