On some new oriented Singquandles and their shadows

A quandle Q is a right distributive right quasi-groupoid where every element is idempotent. This paper focuses on a special type of quandle, namely, oriented singular quandles. This structure arises from the study of oriented singular knots with both regular and singular crossings. While the literature extensively features oriented singquandles derived from the conjugation quandle [Formula: see text], this paper concentrates on constructing new examples of oriented singular quandles from the core quandle [Formula: see text]. We demonstrate the construction of singquandles from specific rings. We have also developed a framework for producing oriented singquandle shadows from modules. Finally, we explore the categorical relationship between a subcategory of oriented singular quandles and the category of semigroups.