Baer rings and quasicontinuous rings have a MDSN
نویسندگان
چکیده
منابع مشابه
A Generalization of Baer Rings
A ringR is called generalized right Baer if for any non-empty subset S of R, the right annihilator rR(S ) is generated by an idempotent for some positive integer n. Generalized Baer rings are special cases of generalized PP rings and a generalization of Baer rings. In this paper, many properties of these rings are studied and some characterizations of von Neumann regular rings and PP rings are ...
متن کاملLocally Compact Baer Rings
Locally direct sums [W, Definition 3.15] appeared naturally in classification results for topological rings (see, e.g.,[K2], [S1], [S2], [S3], [U1]). We give here a result (Theorem 3) for locally compact Baer rings by using of locally direct sums. 1. Conventions and definitions All topological rings are assumed associative and Hausdorff. The subring generated by a subset A of a ring R is denote...
متن کاملGeneralized Baer rings
In [15], Kaplansky introduced Baer rings as rings in which every right (left) annihilator ideal is generated by an idempotent. According to Clark [9], a ring R is called quasi-Baer if the right annihilator of every right ideal is generated (as a right ideal) by an idempotent. Further works on quasi-Baer rings appear in [4, 6, 17]. Recently, Birkenmeier et al. [8] called a ring R to be a right (...
متن کاملOn Commutative Reduced Baer Rings
It is shown that a commutative reduced ring R is a Baer ring if and only if it is a CS-ring; if and only if every dense subset of Spec (R) containing Max (R) is an extremally disconnected space; if and only if every non-zero ideal of R is essential in a principal ideal generated by an idempotent.
متن کاملThe unit sum number of Baer rings
In this paper we prove that each element of any regular Baer ring is a sum of two units if no factor ring of R is isomorphic to Z_2 and we characterize regular Baer rings with unit sum numbers $omega$ and $infty$. Then as an application, we discuss the unit sum number of some classes of group rings.
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1981
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1981.97.283