scholarly journals When Is a Simple Ring Noetherian?

1996 ◽  
Vol 184 (2) ◽  
pp. 786-794 ◽  
Author(s):  
Dinh Van Huynh ◽  
S.K. Jain ◽  
S.R. López-Permouth
Keyword(s):  
Simple Ring

Rings With Involution Whose Symmetric Units Commute

1976 ◽  
Vol 28 (5) ◽  
pp. 915-928 ◽  
Author(s):  
Charles Lanski
Keyword(s):  
Unitary Group ◽  
Simple Ring ◽  
Algebraic Properties ◽  
Rings With Involution ◽  
Additional Assumptions

In the last few years many results have appeared which deal with questions of how various algebraic properties of the symmetric elements of a ring with involution, or the subring they generate, affect the structure of the whole ring. If the ring has an identity, similar questions may be posed by making assumptions about the symmetric units or subgroup they generate. Little seems to be known about the special units which exist in rings with involution, although several questions of importance have existed for some time. For example, given a simple ring with appropriate additional assumptions, is the unitary group essentially simple? Also, what can be said about the structure of subspaces invariant under conjugation by all unitary or symmetric units (see [7])?

Subdirectly Irreducible DQC Rings

1971 ◽  
Vol 14 (4) ◽  
pp. 495-498 ◽  
Author(s):  
W. Burgess ◽  
M. Chacron
Keyword(s):  
Division Ring ◽  
Subdirectly Irreducible ◽  
Simple Ring

AbstractTwenty-five years ago McCoy published a characterization of commutative subdirectly irreducible rings. This result was generalized by Thierrin to duo rings with the word “field” which appeared in McCoy's theorem replaced by “division ring”. The purpose of this note is to give another generalization in which the words “division ring” will be replaced by “simple ring with 1 ”. The techniques resemble those of McCoy and Thierrin.

scholarly journals Unique factorisation rings

1992 ◽  
Vol 35 (2) ◽  
pp. 255-269 ◽  
Author(s):  
A. W. Chatters ◽  
M. P. Gilchrist ◽  
D. Wilson
Keyword(s):  
Prime Ideal ◽  
Prime Ring ◽  
Polynomial Identity ◽  
Noetherian Ring ◽  
Basic Theory ◽  
Maximal Order ◽  
Prime Element ◽  
Polynomial Extension ◽  
Simple Ring ◽  
Left And Right

Let R be a ring. An element p of R is a prime element if pR = Rp is a prime ideal of R. A prime ring R is said to be a Unique Factorisation Ring if every non-zero prime ideal contains a prime element. This paper develops the basic theory of U.F.R.s. We show that every polynomial extension in central indeterminates of a U.F.R. is a U.F.R. We consider in more detail the case when a U.F.R. is either Noetherian or satisfies a polynomial identity. In particular we show that such a ring R is a maximal order, that every height-1 prime ideal of R has a classical localisation in which every two-sided ideal is principal, and that R is the intersection of a left and right Noetherian ring and a simple ring.

scholarly journals Note on simple ring extensions

1976 ◽  
Vol 5 (2) ◽  
pp. 237-238 ◽  
Author(s):  
Sigurd ELLIGER ◽  
Hisao TOMINAGA
Keyword(s):  
Simple Ring ◽  
Ring Extensions

A Simple Ring Oven for Microanalysis

1994 ◽  
Vol 71 (7) ◽  
pp. 606 ◽  
Author(s):  
P. Riyazuddin
Keyword(s):  
Simple Ring ◽  
Ring Oven

X-rays from superbubbles in the Large Magellanic Cloud

1991 ◽  
Vol 148 ◽  
pp. 99-100
Author(s):  
You-Hua Chu ◽  
Mordecai-Mark Mac Low
Keyword(s):  
Large Magellanic Cloud ◽  
Magellanic Cloud ◽  
Shell Structures ◽  
X Rays ◽  
Simple Ring ◽  
X Ray ◽  
Order Of Magnitude

We find diffuse X-ray emission not associated with known SNRs in seven LMC HII complexes. All, except 30 Dor, have simple ring morphologies, indicating shell structures. Assuming these are superbubbles, we find the X-ray luminosity expected from their hot interiors to be an order of magnitude lower than the observed value. SNRs close to the center of a superbubble add very little emission, but we calculate that off-center SNRs hitting the ionized shell could explain the observed emission.

scholarly journals On Brown–McCoy radical classes in categories

1983 ◽  
Vol 26 (3) ◽  
pp. 337-341
Author(s):  
S. Veldsman
Keyword(s):  
Simple Object ◽  
Radical Class ◽  
Topological Spaces ◽  
Modular Class ◽  
Simple Ring ◽  
Object A ◽  
Associative Rings

What does a simple ring with unity, a topological T0-space and a graph that has at most one loop but may possess edges, have in common? In this note we show that they all are Brown–McCoy semisimple. Suliński has generalised the well-known Brown–McCoy radical class of associative rings (cf. [1]) to a category which satisfies certain conditions. In [3] he defines a simple object, a modular class of objects and the Brown–McCoy radical class as the upper radical class determined by a modular class in a category which, among others, has a zero object and kernels. To include categories like that of topological spaces and graphs, we use the concepts of a trivial object and a fibre. We then follow Suliński and define a simple object, a modular class of objects and then the Brown–McCoy radical class as the upper radical class determined by a modular class.

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