On Rings of MAL'CEV-NEUMANN Series
Mohammad. H. Fahmy, Refaat. M. Salem, Shaimaa. Sh. Shehata
TL;DR
This paper explores the algebraic properties of Mal'cev-Neumann series rings, specifically their conditions for being left fusible and SA-rings, and characterizes when they are zip rings based on group and ideal properties.
Contribution
It provides new criteria for Mal'cev-Neumann series rings to be left fusible, SA-rings, and zip rings, linking these properties to group orderings and ideal compatibility.
Findings
Conditions for Mal'cev-Neumann series rings to be left fusible.
Criteria for these rings to be SA-rings.
Characterization of zip ring conditions based on group and ideal properties.
Abstract
In this paper, we investigate the conditions for the Mal'cev-Neumann series ring {\Lambda} = R((G;{\sigma};{\tau})) to be left fusible and an SA-ring. Also, we show that: if G is a quasitotally ordered group and U a {\Sigma}-compatible semiprime ideal of R, then R((G;{\sigma};{\tau})) is a {\Sigma}(U((G; {\sigma}; {\tau})))-zip ring if and only if R is a {\Sigma}(U )-zip ring.
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Taxonomy
TopicsCoding theory and cryptography · Rings, Modules, and Algebras