Abstract: Let R be a unital simple Artinian ring with center Z and involution f. By an invariant multiplicative subset of R, we mean a subset of R written as M with the following properties: (i) 1 ∈ M, (ii) M is closed under multiplication, (iii) M is invariant under f, and (iv) M is invariant under all inner automorphisms of R. Define the trace (res. norm) of a given subset X of R written as tr X (res. nr X) to be the set of all elementary traces (res. norms) as x ranges over X. In this paper, we investigate the case in which the considered invariant multiplicative subset M has central trace but M is not contained in Z. Substantive information about the structure of R and the type of f has been provided. |
Keywords and phrases: simple Artinian ring, invariant multiplicative subset, trace, norm, involution.
Received: August 14, 2021; Accepted: September 20, 2021; Published: February 14, 2022
How to cite this article: Maurice Chacron, Certain invariant multiplicative subset of a simple Artinian ring with involution, JP Journal of Algebra, Number Theory and Applications 53(2) (2022), 151-163. DOI: 10.17654/0972555522009
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
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