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Keywords
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Centrally morphic ring, idempotent, morphic ring, quasi-morphic
ring, regular ring, strongly regular ring, unit-regular ring
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Abstract
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The main objective of this paper is to study (quasi-)morphic prop-
erty of skew polynomial rings.
Let R be a ring, σ be a ring homomor-
phism on R and n ≥ 1. We show that R inherits the quasi-morphic prop-
erty from R[x;σ]/(xn+1). It is also proved that the morphic property over
R[x;σ]/(xn+1) implies that R is a regular ring. Moreover, we characterize a
unit-regular ring R via the morphic property of R[x;σ]/(xn+1). We also inves-
tigate the relationship between strongly regular rings and centrally morphic
rings. For instance, we show that for a domain R, R[x;σ]/(xn+1) is (left)
centrally morphic if and only if R is a division ring and σ(r) = u−1ru for some
u ∈ R. Examples which delimit and illustrate our results are provided
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