On Closedness of Subvarieties of Bands

Document Type : Research Paper

Authors

Department of Mathematics‎, ‎Aligarh Muslim University‎, ‎Aligarh‎, ‎India

Abstract

In this paper‎, ‎first we proved that all subvarieties of the variety of left (right) regular bands are closed in the variety of $n$-nilpotent extension of bands‎. ‎Secondly‎, ‎we proved the closedness of rectangular bands in the variety $\mathcal{V}=[ac=ab^nc]$ $(n\in \bf N)$‎, ‎of semigroups‎. ‎Further‎, ‎we have shown that all subvarieties of the variety of left (right) normal bands are closed in the variety $\mathcal{V}=[axy=a^py^qx^r]$ $(p,q,r\in \bf N)$‎, ‎of semigroups and lastly‎, ‎we proved that all subvarieties of the variety of left (right) quasinormal bands are closed in the variety $\mathcal{V}=[axy=a^px^qa^ry]$ $(p,q,r\in \bf N)$‎,‎ of semigroups.

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References

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