University of Guilan Journal of Algebra and Related Topics 2345-3931 14 Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024). 2026 04 01 On Closedness of Subvarieties of Bands 235 245 9526 10.22124/jart.2026.27992.1692 EN Sh. Abbas Department of Mathematics‎, ‎Aligarh Muslim University‎, ‎Aligarh‎, ‎India W. Ashraf Department of Mathematics‎, ‎Aligarh Muslim University‎, ‎Aligarh‎, ‎India A. Prakash Department of Mathematics‎, ‎Aligarh Muslim University‎, ‎Aligarh‎, ‎India Journal Article 2024 07 22 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. https://jart.guilan.ac.ir/article_9526_9ad7dca10cbf269e3feeff1de29fb84a.pdf