Class of Baer ∗-rings defined by a relaxed set of axioms
نویسندگان
چکیده
منابع مشابه
Dimension and Torsion Theories for a Class of Baer *-Rings
Many known results on finite von Neumann algebras are generalized, by purely algebraic proofs, to a certain class C of finite Baer *-rings. The results in this paper can also be viewed as a study of the properties of Baer *-rings in the class C. First, we show that a finitely generated module over a ring from the class C splits as a direct sum of a finitely generated projective module and a cer...
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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 ...
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In this paper, we introduce a class of $J$-quasipolar rings. Let $R$ be a ring with identity. An element $a$ of a ring $R$ is called {it weakly $J$-quasipolar} if there exists $p^2 = pin comm^2(a)$ such that $a + p$ or $a-p$ are contained in $J(R)$ and the ring $R$ is called {it weakly $J$-quasipolar} if every element of $R$ is weakly $J$-quasipolar. We give many characterizations and investiga...
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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 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: Journal of Algebra
سال: 2006
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2005.07.022