Zero commutativity of nilpotent elements skewed by ring endomorphisms

ABSTRACT

The reversible property is an important role in noncommutative ring theory. Recently, the study of the reversible ring property on nilpotent elements is established by Abdul-Jabbar et al., introducing the concept of commutativity of nilpotent elements at zero (simply, a CNZ ring) as a generalization of reversible rings. We here study this property skewed by a ring endomorphism α, and such ring is called a right α-skew CNZ ring which is an extension of CNZ rings as well as a generalization of right α-skew reversible rings, and then investigate the structure of right α-skew CNZ rings and their related properties. Consequently, several known results are obtained as corollaries of our results.

KEYWORDS:

• (Right skew) CNZ ring
• matrix ring
• (skew) polynomial ring
• (skew) power series ring
• reversible ring

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16U80
• 16W20
• 16N40