in this article, we study the artin-rees property in  c(x), in the  rings of fractions of  c(x) and in the factor rings of c(x) . we show that c(x)/(f) is an artin-rees ring if and only if  z(f)  is an open p-space. a necessary and sufficient condition for the local rings of  c(x)   to be artin-rees rings is that each prime ideal in  c(x)  becomes minimal and it turns out that every local ring ...

In this paper, we study Lie and Jordan Structure in Simple Γ− Regular Ring of characteristic not equal to two. Some Properties of these Γ− Regular Ring are determined.

LetR be a von Neumann regular ring. The main results of this paper assert whether a von Neumann regular ring is expressible as a directed union of finite products of fields.

Let n | m be positive integers with the same prime factors, such that p3 | n for some prime p. We construct a noncrossed product division algebra D with involution ∗, of index m and exponent n, such that D possesses a Baer ordering relative to the involution ∗. Using similar techniques we construct indecomposable division algebras with involution possessing a Baer

Reinhold Baer asked the relationship between certain properties in a nonempty set P with a partial operation (called an “add" by Baer [1]). The first paper in our sequence [Paper I] answered his question for a special type of an add called a pregroup by Stallings [12]. This paper [Paper II] answers an analogous question for a wider class of adds.

Thirty two patients between 6 months and 14 years of age with tubercular meningitis were evaluated for brain stem auditory evoked response (BAER) and Visual evoked responses (VER), within 7 days of admission. Absolute latencies and interpeak latencies were compared with values obtained from normal children. BAER abnormality was found in 56.25% and VER in 28%children, respectively. BAER abnormal...

In [6], the compatibility of Baer involutions and elations was studied. Further compatibility results for translation planes of dimension 2 were obtained in [10]. For example [6, Theorem (2.2)], we have the following. Let n be a derivable translation plane of even order q, q # 2, with derivable net N. Let EL denote an elation group in the translation complement which fixes the component L of N ...

In this paper we introduce the notion of unit-regular ideals for unital rings, which is a natural generalization of unit-regular rings. It is shown that every square matrix over unit-regular ideals admits a diagonal reduction. We also prove that a regular ideal of a unital ring is unit-regular if and only if pseudo-similarity via the ideal is similarity. Let I be an ideal of a unital ring R. We...

It is well known that a commutative ring R is complemented (that is, given a ∈ R there exists b ∈ R such that ab = 0 and a + b is a regular element) if an only if the total ring of quotients of R is von Neumann regular. We consider generalizations of the notion of a complemented ring and their implications for the total ring of quotients. We then look at the specific case when the ring is a rin...