Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 43, No. 2, pp. 423-432 (2002)

On Subdirect Decomposition and Varieties of Some Rings with Involution

Sinisa Crvenkovic, Igor Dolinka, Milovan Vincic

Institute of Mathematics, Faculty of Science, University of Novi Sad, Trg Dositeja Obradovica 4, 21000 Novi Sad, Yugoslavia, e-mail: sima@eunet.yu, e-mail:; Department of Mathematics, Faculty of Mechanical Engineering, University of Banja Luka, Danka Mitrova 10, 78000 Banja Luka, Bosnia and Herzegovina

Abstract: We give a complete description of subdirectly irreducible rings with involution satisfying $x^{n+1}=x$ for some positive integer $n$. We also discuss ways to apply this result for constructing lattices of varieties of rings with involution obeying an identity of the given type.

Keywords: ring with involution, field, subdirectly irreducible, variety

Classification (MSC2000): 16W10, 08B26, 08B15

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