Krull dimension of modules over involution rings. II

Beidar, K.; Puczylowski, E.; Smith, P.

doi:10.1090/S0002-9939-97-03724-6

Krull dimension of modules over involution rings. II
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by K. I. Beidar, E. R. Puczylowski and P. F. Smith PDF

Proc. Amer. Math. Soc. 125 (1997), 355-361 Request permission

Abstract:

Let $R$ be a ring with involution and invertible 2, and let $\bar S$ be the subring of $R$ generated by the symmetric elements in $R$. The following questions of Lanski are answered positively:

[(i)] Must $\bar S$ have Krull dimension when $R$ does?

[(ii)] Is every Artinian $R$-module Artinian as an $\bar S$-module?

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