Semiprime Novikov algebras

A. Panasenko
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引用次数: 3

Abstract

. We study prime and semiprime Novikov algebras. We prove that prime nonassociative Novikov algebra has zero nucleus and center. It is well known that an ideal of an alternative (semi)prime algebra is (semi)prime algebra. We proved this statement for Novikov algebras. It implies that a Baer radical exists in a class of Novikov algebras. Also, we proved that a minimal ideal of Novikov algebra is either trivial, or a simple algebra.
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。我们学习素数和半素数Novikov代数。证明了素数非结合诺维科夫代数具有零核和零中心。众所周知,一个可选的半素数代数的理想是半素数代数。我们用诺维科夫代数证明了这个命题。证明了一类Novikov代数中存在Baer根。同时,我们证明了Novikov代数的极小理想要么是平凡代数,要么是简单代数。
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