Some properties of AG^*-groupoids and AG-bands under SI-product operation

Article type: Research Article

Authors: Karaaslan, Faruk^{; *}

Affiliations: Department of Mathematics, Faculty and Sciences, Çankırı Karatekin University, 18100 Çankırı, Turkey

Correspondence: [*] Corresponding author. F. Karaaslan, Department of Mathematics, Faculty and Sciences, Çankırı Karatekin University, 18100 Çankırı, Turkey, E-mail: fkaraaslan@karatekin.edu.tr.

Abstract: The concepts of AG*-groupoid and AG-band are two subclasses of AG-groupoids. In this study, some properties of family of soft sets over AG-groupoid, AG*-groupoid and AG-band are investigated. It is proved that family of soft sets over AG-groupoid is an AG-groupoid and family of soft sets over AG*-groupoid is both nuclear square AG-groupoid and Bol*-AG-groupoid under SI-product operation. Also some new concepts such as soft idempotent element, soft intersection AG-band, left(right) connected soft set, soft intersection-ideal and soft prime ideal of soft intersection AG-groupoid are defined and some results related to these new concepts are obtained.

Keywords: Soft set, soft intersection AG-groupoid, soft intersection AG-band, soft intersection ideal.

DOI: 10.3233/JIFS-181208

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 1, pp. 231-239, 2019