In this work we deal with coverings and actions of Lie groupgroupoids being a sort of the structured Lie groupoids. Firstly, we define an action of a Lie group-groupoid on some Lie group and the smooth coverings of Lie group-groupoids. Later, we show the equivalence of the category of smooth actions of Lie group-groupoids on Lie groups and the category of smooth coverings of Lie group-groupoids.

Cyclic associative groupoids (CA-groupoids) and Type-2 cyclic (T2CA-groupoids) are two types of non-associative which satisfy law type-2 law, respectively. In this paper, we prove theorems that weak cancellativity is right quasi-cancellativity left in a CA-groupoid, thus successfully solving open problems. Moreover, the relationships among separativity, commutativity CA-groupoid discussed. Fina...

The quasivariety of groupoids [Formula: see text] satisfying the implication [Formula: see text] generalises rectangular semigroups and central groupoids. We call them rectangular groupoids and find three combinatorial structures based upon arrays, matrices and graphs that are closely related. These generalise several groupoids of independent interest. The quasivariety generates the variety of ...

This paper deals with Lie groupoids, in particular symplectic and contact groupoids. We formulate a deenition of contact groupoids; we give examples and a counterexample (groupoid with a contact form which is not a contact groupoid). The theory of diierentiable groupoids (called now Lie groupoids) has been introduced by C. Ehresmann E] in 1950 in his paper on connections (where he deened the gr...

In this paper we introduce the concept of ideal elements in poe-AG-groupoid and give some characterizations and properties of their ideal elements. So we consider some results concerning ideals in poe-semigroups and investigate them in poe-AG-groupoids. Also, the class of ideal elements of poe-AG-groupoids are studied, certain intrinsic and basic properties of poe-AG-groupoids including: ideal,...

We describe a part of the lattice of subvarieties of left distributive left idempotent groupoids (i.e. those satisfying the identities x(yz) ≈ (xy)(xz) and (xx)y ≈ xy) modulo the lattice of subvarieties of left distributive idempotent groupoids. A free groupoid in a subvariety of LDLI groupoids satisfying an identity x ≈ x decomposes as the direct product of its largest idempotent factor and a ...

In this paper we introduced the notions of uni-soft AG-groupoids, uni-soft left(right) ideals and uni-soft quasi ideals of AG-groupoids and also investigated related properties of these structures. Some interesting Characterizations of uni-soft AG-groupoids and uni-soft left(right) ideals have been explored. Mathematics Subject Classification: 42B20, 42B25, 46E30