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- Title
REGULARITY AND STRONG REGULARITY IN THE CONTEXT OF CERTAIN CLASSES OF RINGS.
- Authors
ZIEMBOWSKI, MICHAL
- Abstract
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, Bezout rings, Gaussian rings, quasi-morphic rings, semihereditary rings, and rings which have weak dimension less than or equal to one.
- Subjects
MATHEMATICAL regularization; RING theory; POLYNOMIALS; VON Neumann regular rings; GAUSSIAN function; INTEGERS
- Publication
Journal of Algebra & Its Applications, 2013, Vol 12, Issue 5, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498812502052