scholarly journals Left Rings

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Junchao Wei
Keyword(s):  
Left Ideal ◽  
Strongly Regular ◽  
Maximal Left Ideal ◽  
Regular Rings

We introduce in this paper the concept of left rings and concern ourselves with rings containing an injective maximal left ideal. Some known results for left idempotent reflexive rings and left rings can be extended to left rings. As applications, we are able to give some new characterizations of regular left self-injective rings with nonzero socle and extend some known results on strongly regular rings.

scholarly journals MC2 RINGS AND WQD RINGS

2009 ◽  
Vol 51 (3) ◽  
pp. 691-702 ◽  
Author(s):  
JUNCHAO WEI ◽  
LIBIN LI
Keyword(s):  
Left Ideal ◽  
Strongly Regular ◽  
Maximal Left Ideal ◽  
Regular Rings

AbstractWe introduce in this paper the concepts of rings characterized by minimal one-sided ideals and concern ourselves with rings containing an injective maximal left ideal. Some known results for idempotent reflexive rings and left HI rings can be extended to left MC2 rings. As applications, we are able to give some new characterizations of regular left self-injective rings with non-zero socle and extend some known results for strongly regular rings.

scholarly journals Simplex algebras and their representation

1973 ◽  
Vol 14 (2) ◽  
pp. 136-144
Author(s):  
M. S. Vijayakumar
Keyword(s):  
Left Ideal ◽  
Maximal Ideal ◽  
Banach Algebras ◽  
Principal Component ◽  
Nonempty Interior ◽  
Regular Elements ◽  
Maximal Left Ideal ◽  
The Relationship ◽  
Order Identity ◽  
Real Matrices

This paper establishes a relationship (Theorem 4.1) between the approaches of A. C. Thompson [8, 9] and E. G. Effros [2] to the representation of simplex algebras, that is, real unital Banach algebras that are simplex spaces with the unit for order identity. It proves that the (nonempty) interior of the associated cone is contained in the principal component of the set of all regular elements of the algebra. It also conjectures that each maximal ideal (in the order sense—see below) of a simplex algebra contains a maximal left ideal of the algebra. This conjecture and other aspects of the relationship are illustrated by considering algebras of n × n real matrices.

scholarly journals A note on strongly regular rings

1964 ◽  
Vol 40 (2) ◽  
pp. 74-75
Author(s):  
Jiang Luh
Keyword(s):  
Strongly Regular ◽  
Regular Rings

Some Remarks on Regular and Strongly Regular Rings

1975 ◽  
Vol 17 (5) ◽  
pp. 709-712 ◽  
Author(s):  
R. Raphael
Keyword(s):  
Generalized Inverse ◽  
Ring Homomorphisms ◽  
Strongly Regular ◽  
Regular Rings

This article presents some new algebraic and module theoretic characterizations of strongly regular rings. The latter uses Lambek’s notion of symmetry. Strongly regular rings are shown to admit an involution and form an equational category. An example due to Paré shows that the category of regular rings and ring homomorphisms between them is not equational. Remarks on quasiinverses and the generalized inverse of a matrix are included. The author acknowledges support from the NRC (A7752) and improvements from W. Blair received after announcement of the results.

A generalization of strongly regular rings

1984 ◽  
Vol 43 (1-2) ◽  
pp. 57-61 ◽  
Author(s):  
V. Gupta
Keyword(s):  
Strongly Regular ◽  
Regular Rings

Strongly regular rings

1985 ◽  
Vol 32 (1) ◽  
pp. 145-161
Author(s):  
Lide Li ◽  
Boris M. Schein
Keyword(s):  
Strongly Regular ◽  
Regular Rings

scholarly journals REDUCED MODULES AND STRONGLY REGULAR RINGS

2017 ◽  
Vol 33 (1) ◽  
pp. 75-81
Author(s):  
Chan Huh ◽  
Jeoung Soo Cheon ◽  
Du Won Kim
Keyword(s):  
Strongly Regular ◽  
Regular Rings
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