Non-Commutative Ring Theory

1990 ◽  
Keyword(s):  
Commutative Ring ◽  
Ring Theory ◽  
Commutative Ring Theory

scholarly journals Examples and Counterexamples in Commutative Ring Theory

1995 ◽  
Vol 172 (3) ◽  
pp. 744-763 ◽  
Author(s):  
S.S. Abhyankar ◽  
W.J. Heinzer
Keyword(s):  
Commutative Ring ◽  
Ring Theory ◽  
Commutative Ring Theory

László Fuchs’s contributions to commutative ring theory

2014 ◽  
Vol 69 (1) ◽  
pp. 2-8
Author(s):  
Bruce Olberding ◽  
Kulumani M. Rangaswamy
Keyword(s):  
Commutative Ring ◽  
Ring Theory ◽  
Commutative Ring Theory

scholarly journals ON THE NOTION OF STRONG IRREDUCIBILITY AND ITS DUAL

2013 ◽  
Vol 12 (06) ◽  
pp. 1350012 ◽  
Author(s):  
JAWAD ABUHLAIL ◽  
CHRISTIAN LOMP
Keyword(s):  
Commutative Ring ◽  
Theoretical Approach ◽  
Associative Ring ◽  
Ring Theory ◽  
Irreducible Elements ◽  
Strongly Irreducible ◽  
Torsion Theories ◽  
Commutative Ring Theory ◽  
Strong Irreducibility

This note gives a unifying characterization and exposition of strongly irreducible elements and their duals in lattices. The interest in the study of strong irreducibility stems from commutative ring theory, while the dual concept of strong irreducibility had been used to define Zariski-like topologies on specific lattices of submodules of a given module over an associative ring. Based on our lattice theoretical approach, we give a unifying treatment of strong irreducibility, dualize results on strongly irreducible submodules, examine its behavior under central localization and apply our theory to the frame of hereditary torsion theories.

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