Left Self Distributively Generated Structural Matrix Rings

2005 ◽  
Vol 33 (9) ◽  
pp. 2865-2877
Author(s):  
John A. Lewallen
Keyword(s):  
Matrix Rings ◽  
Structural Matrix

scholarly journals On the small and essential ideals in certain classes of rings

1989 ◽  
Vol 46 (2) ◽  
pp. 262-271 ◽  
Author(s):  
B. W. Green ◽  
L. van Wyk
Keyword(s):  
Commutative Rings ◽  
Matrix Rings ◽  
Small Ideal ◽  
Prufer Domains ◽  
Prüfer Domains ◽  
Complete Matrix ◽  
Structural Matrix

AbstractIt is well known that for a ring with identity the Brown-McCoy radical is the maximal small ideal. However, in certain subrings of complete matrix rings, which we call structural matrix rings, the maximal small and minimal essential ideals coincide.In this paper we characterize a class of commutative and a class of non-commutative rings for which this coincidence occurs, namely quotients of Prüfer domains and structural matrix rings over Brown-McCoy semisimple rings. A similarity between these two classes is obtained.

Invertibility and Dedekind finiteness in structural matrix rings

2011 ◽  
Vol 59 (2) ◽  
pp. 221-227 ◽  
Author(s):  
Stephan Foldes ◽  
Jenő Szigeti ◽  
Leon van Wyk
Keyword(s):  
Matrix Rings ◽  
Structural Matrix

scholarly journals OPTIMIZATION OF MATRIX SEMIRINGS FOR CLASSIFICATION SYSTEMS

2011 ◽  
Vol 84 (3) ◽  
pp. 492-503 ◽  
Author(s):  
D. Y. GAO ◽  
A. V. KELAREV ◽  
J. L. YEARWOOD
Keyword(s):  
Discrete Event Systems ◽  
Discrete Event ◽  
Classification Systems ◽  
Second Main Theorem ◽  
Matrix Rings ◽  
Multiple Classifiers ◽  
Generating Sets ◽  
Event Systems ◽  
First Main Theorem ◽  
Structural Matrix

AbstractThe max-plus algebra is well known and has useful applications in the investigation of discrete event systems and affine equations. Structural matrix rings have been considered by many authors too. This article introduces more general structural matrix semirings, which include all matrix semirings over the max-plus algebra. We investigate properties of ideals in this construction motivated by applications to the design of centroid-based classification systems, or classifiers, as well as multiple classifiers combining several initial classifiers. The first main theorem of this paper shows that structural matrix semirings possess convenient visible generating sets for ideals. Our second main theorem uses two special sets to determine the weights of all ideals and describe all matrix ideals with the largest possible weight, which are optimal for the design of classification systems.

scholarly journals Induced good gradings of structural matrix rings

2019 ◽  
Vol 47 (3) ◽  
pp. 1114-1124
Author(s):  
John Dewitt ◽  
Kenneth L. Price
Keyword(s):  
Matrix Rings ◽  
Structural Matrix

scholarly journals Some remarks on structural matrix rings and matrices with ideal entries

2011 ◽  
Vol 12 (1) ◽  
pp. 25
Author(s):  
Stephan Foldes ◽  
Gerasimos Meletiou
Keyword(s):  
Matrix Rings ◽  
Structural Matrix

scholarly journals On p.p. structural matrix rings

2012 ◽  
Vol 436 (9) ◽  
pp. 3692-3700 ◽  
Author(s):  
Chunna Li ◽  
Yiqiang Zhou
Keyword(s):  
Matrix Rings ◽  
Structural Matrix

Polynomial regularities in structural matrix rings

1994 ◽  
Vol 22 (6) ◽  
pp. 2101-2123 ◽  
Author(s):  
N.J. Groenewald ◽  
L. Van Wyt
Keyword(s):  
Matrix Rings ◽  
Structural Matrix
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