Abstract
In the first part of the paper, we provide a fairly complete description of a simple ring R with involution f such that relative to f the traces of all elements of R form a commutative subset of R. This description is based on the characteristic of R. While the case of characteristic not 2 readily follows from current results in the literature, by contrast, the opposite case of characteristic 2 requires markedly more work. In the rest of the paper, the results carried out earlier are put to work to delineate the structure of a simple Artinian ring R with involution f, which is equipped with a given non central multiplicative subset M stabilized by f and preserved by all inner automorphisms of R, and such that the traces relative to f of all elements of M form a commutative subset of R.
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Acknowledgement
The author is indebted to the referee for a careful reading of the paper, for a simplification in the proof of Lemma 4, and for varied suggestions to reach out to the reader.
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Chacron, M. Certain invariant multiplicative subset of a simple Artinian ring with involution. II. Acta Math. Hungar. 170, 437–454 (2023). https://doi.org/10.1007/s10474-023-01355-1
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DOI: https://doi.org/10.1007/s10474-023-01355-1