Krull dimension of modules over involution rings

Beĭdar, K. I.; Puczyłowski, E. R.; Smith, P. F.

doi:10.1090/S0002-9939-1994-1184081-3

Krull dimension of modules over involution rings
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by K. I. Beĭdar, E. R. Puczyłowski and P. F. Smith PDF

Proc. Amer. Math. Soc. 121 (1994), 391-397 Request permission

Abstract:

The following question of Lanski is answered positively in the case when a ring R with involution $^ \ast$ is Noetherian with respect to two-sided $\ast$-ideals. Let R be a ring with $^ \ast$ and invertible 2, and let $\bar S$ be the subring of R generated by the symmetric elements in R. Does any left R-module have the same Krull dimension when considered as an R-module and $\bar S$-module?

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