Characterizations of reversible rings relating k-potents

This article embodies a ring theoretic property that preserves the reversibility at non zero k-potents. The structure of k-potents in k-reversible and pseudo k-reversible rings are studied in connection with various kinds of ring extensions. A ring R is said to be k-reversible if and only if ab ∈ K(R) for a,b ∈ R implies ab = ba; and a ring R is called pseudo k-reversible if 0 ̸= ab ∈ K(R) for a,b ∈ K(R) implies ab = ba, where K(R) is the set of all k-potents in R. It is proved that k-reversible rings are pseudo k-reversible but the converse is not true in general. Under certain conditions the polynomial rings of pseudo k-reversible inherit the character of pseudo k-reversible rings.