JP Journal of Algebra, Number Theory and Applications
Volume 45, Issue 1, Pages 101 - 119
(January 2020) http://dx.doi.org/10.17654/NT045010101 |
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ON STRONG SYMMETRIC RINGS AND THEIR EXTENSIONS
Wafaa Mohammed Fakieh
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Abstract: Lambek called a ring R symmetric if whenever then for In this paper, we study an extension of symmetric ring with its endomorphism. An endomorphism α of a ring R is called strong right (resp., left) symmetric if whenever for A ring R is called strong right (resp., left) α-symmetric if there exists a strong right (resp., left) symmetric endomorphism α of R, and the ring R is called strong α-symmetric if R is both strong left and right α-symmetric. We study characterizations of strong α-symmetric rings and their related properties including extensions. In particular, we show that every semiprime and strong α-symmetric ring is α-rigid and we prove that if R is an α-skew Armendariz ring, then R is symmetric and strong α-symmetric if and only if the skew polynomial ring of R is symmetric. |
Keywords and phrases: α-symmetric ring, α-rigid ring, α-skew Armendariz ring, strong α-symmetric ring.
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