Commutativity and ideals in algebraic crossed products
Johan Oinert (1, 2), Sergei D. Silvestrov (2) ((1) University of, Antwerp, (2) Lund University)
TL;DR
This paper explores the structure of commutative subrings and ideals within non-commutative algebraic crossed products, providing criteria for commutativity and maximal commutativity based on group actions and ideal intersections.
Contribution
It offers a detailed description of the commutant of the base subring and establishes conditions for commutativity in crossed products considering zero-divisors.
Findings
Characterization of the commutant of the base subring
Conditions for commutativity and maximal commutativity
Analysis of ideals intersection with the base subring
Abstract
We investigate properties of commutative subrings and ideals in non-commutative algebraic crossed products for actions by arbitrary groups. A description of the commutant of the base coefficient subring in the crossed product ring is given. Conditions for commutativity and maximal commutativity of the commutant of the base subring are provided in terms of the action as well as in terms of the intersection of ideals in the crossed product ring with the base subring, specially taking into account both the case of base rings without non-trivial zero-divisors and the case of base rings with non-trivial zero-divisors.
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