Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 41, No. 2, pp. 325-328 (2000)

Varieties and Sums of Rings

A. V. Kelarev

School of Mathematics, University of Tasmania, G.P.O. Box 252-37, Hobart, Tasmania 7001, Australia, e-mail:

Abstract: For commutative algebras over a field, we describe all varieties closed for taking algebras which are sums of their two subalgebras in the variety.

Keywords: varieties, sums of algebras

Classification (MSC2000): 16R10; 16S99

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