Commun. Korean Math. Soc. 2024; 39(2): 373-397
Online first article April 25, 2024 Printed April 30, 2024
https://doi.org/10.4134/CKMS.c230292
Copyright © The Korean Mathematical Society.
Fatma Kaynarca , H. Melis Tekin Akcin
Afyon Kocatepe University; Halise Melis Tekin Akcin
Lambek introduced the concept of symmetric rings to expand the commutative ideal theory to noncommutative rings. In this study, we propose an extension of symmetric rings called strongly $\alpha$-symmetric rings, which serves as both a generalization of strongly symmetric rings and an extension of symmetric rings. We define a ring $R$ as strongly $\alpha$-symmetric if the skew polynomial ring $R[x;\alpha]$ is symmetric. Consequently, we provide proofs for previously established outcomes regarding symmetric and strongly symmetric rings, directly derived from the results we have obtained. Furthermore, we explore various properties and extensions of strongly $\alpha$-symmetric rings.
Keywords: Strongly $\alpha$-symmetric ring, (strongly) symmetric ring, $\alpha$-rigid ring, $\alpha$-compatible ring, polynomial ring, skew polynomial ring, classical left quotient ring, Jordan extension, Dorroh extension
MSC numbers: Primary 16W20; Secondary 16U80, 16S36
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