REGULARITY AND STRONG REGULARITY IN THE CONTEXT OF CERTAIN CLASSES OF RINGS
2013 ◽
Vol 12
(05)
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pp. 1250205
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Keyword(s):
We consider the ring R[x]/(xn+1), where R is a ring, R[x] is the ring of polynomials in an indeterminant x, (xn+1) is the ideal of R[x] generated by xn+1 and n is a positive integer. The aim of this paper is to show that regularity or strong regularity of a ring R is necessary and sufficient condition under which the ring R[x]/(xn+1) is an example of a ring which belongs to some important classes of rings. In this context, we discuss distributive rings, Bézout rings, Gaussian rings, quasi-morphic rings, semihereditary rings, and rings which have weak dimension less than or equal to one.
2020 ◽
Vol 12
(03)
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pp. 2050045
2018 ◽
Vol 14
(05)
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pp. 1487-1503
1964 ◽
Vol 16
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pp. 310-314
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1970 ◽
Vol 22
(6)
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pp. 1097-1100
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2019 ◽
Vol 101
(2)
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pp. 255-265
2017 ◽
Vol 13
(05)
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pp. 1083-1094
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2013 ◽
Vol Vol. 15 no. 2
(Combinatorics)
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