Dominions and closed varieties of bands

Abstract

We show that all subvarieties of the variety of rectangular bands are closed in the variety of $n$-nilpotent extension of bands. Ahanger, Nabi and Shah in [1] have proved that the variety of regular bands is closed. In this paper, we improve this result and provide its simple and shorter proof. Finally, we show that all subvarieties of the variety of normal bands are closed in the variety of left [right] semiregular bands.