Bezout Rings,Polynomials, and Distributivity |
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Authors: | Tuganbaev A A |
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Institution: | (1) Moscow Power Engineering Institute, Russia |
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Abstract: | Let A be a ring, be an injective endomorphism of A, and let
be the right skew polynomial ring. If all right annihilator ideals of A are ideals, then R is a right Bezout ring
is a right Rickartian right Bezout ring, (e)=e for every central idempotent e A, and the element (a) is invertible in A for every regular a A. If A is strongly regular and n 2, then R/x
n
R is a right Bezout ring
R/x
n
R is a right distributive ring
R/x
n
R is a right invariant ring
(e)=e for every central idempotent e A. The ring R/x
2
R is right distributive
R/x
n
R is right distributive for every positive integer n
A is right or left Rickartian and right distributive, (e)=e for every central idempotent e A and the (a) is invertible in A for every regular a A. If A is a ring which is a finitely generated module over its center, then Ax] is a right Bezout ring
Ax]/x
2
Ax] is a right Bezout ring
A is a regular ring. |
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Keywords: | skew polynomial ring Bezout ring distributive ring |
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