Algebraic aspects of general free skew extensions of rings
Vitor O. Ferreira, \'Erica Z. Fornaroli, Javier S\'anchez
TL;DR
This paper investigates algebraic properties of skew free extensions of rings, providing characterizations and conditions for these rings to be domains, embeddable in series rings, and prime, thus advancing understanding of their structure.
Contribution
It offers new characterizations and criteria for skew free extensions of rings, enhancing the theoretical framework of noncommutative polynomial rings.
Findings
Conditions for skew free extensions to be domains
Criteria for embeddability in series rings
Characterizations of primeness in such rings
Abstract
We consider skew free extensions of rings, also known as free multivariate skew polynomial rings, and explore some of the algebraic aspects of this construction. We give different characterizations of such rings and present conditions for such a ring to be a domain, to be embeddable in a series ring and to be prime.
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