Matricial Closure

2018/05/08 by Murphy-Hernandez, Frank, Raggi, Francisco, Rios, Jose
#16D90 #16E50 #FOS: Mathematics #Primary 16S50 #Rings and Algebras (math.RA) #Secondary 16D25

paper · doi:10.48550/arxiv.1805.03299

Abstract

We study a closure operator derived from the matrix endofunctor on the category of rings with unity. We investigate the invariance of various ring-theoretic properties under this operator. A key finding is the decisive nature of this operator: a property is either preserved for all rings or fails for all rings. This work provides a comprehensive analysis of the behavior of ring properties under matricial closure, including chain conditions, radical-theoretic properties, and other structural characteristics.

Related

• Closure-interior duality over complete local rings
• Topics on strict closure of rings
• Integral closure, basically full closure, and duals of nonresidual closure operations
• Linear Algebra Over a Ring
• Structure on the set of closure operations of a commutative ring