ON QUASI-REFLEXIVE RINGS AND SEMIGROUPS

Abstract

In this note we sharpen most of the results given in [7]. We show for example that the class of right quasi-reflexive rings [semigroups with 0] and the class of left quasi-reflexive ones, investigated in [7] separately, coincide both with the class defined by quasi-reflexivity, a property which seems to be weaker at the first glance. Moreover, the first theorem provides various new examples of quasi-reflexive rings and semigroups with 0, proving that these classes are rather extensive.