Abstract
A groupoid is called power-commutative if every mono-generated subgroupoid is commutative. The class Pc of power-commutative groupoids is a variety. A description of free objects in this variety and their characterization by means of injective groupoids in Pc are obtained.
References
[1] BRUCK, R. H.: A Survey of Binary Systems, Springer-Verlag, Berlin-G¨otingen-Heidelberg, 195810.1007/978-3-662-35338-7Suche in Google Scholar
[2] CELAKOSKA-JORDANOVA,V.: Free groupoids in the class of power left and right idempotent groupoids, Int. J. Algebra 2 (2008), 451-461.Suche in Google Scholar
[3] ČUPONA, G.-CELAKOSKI, N.-ILIĆ, S.: Groupoid powers, Mat. Bilten 25 (2001), 5-12.Suche in Google Scholar
[4] ČUPONA, G.-CELAKOSKI, N.-ILIĆ, S.: On monoassociative groupoids, Mat. Bilten 26 (2002), 5-16.Suche in Google Scholar
[5] ČUPONA, G.-CELAKOSKI, N.-JANEVA, B.: Injective groupoids in some varieties of groupoids. In: Proc. of II Congress of SMIM 2000, 2003, pp. 47-55.Suche in Google Scholar
[6] ČUPONA, G.-ILIĆ, S.: Free groupoids with xn = x, II, NoviSad J. Math. 29 (1999), 147-154.Suche in Google Scholar
[7] KÜHR, J.- MUNDICI, D.: From free abelian groups to free abelian l -groups, Math. Slovaca 61 (2011), 439-450.10.2478/s12175-011-0022-5Suche in Google Scholar
[8] McKENZIE, R. N.-McNULTY, G. F.-TAYLOR, W. F.: Algebras, Lattices, Varieties, Wadsworth & Brooks/Cole, Monterey, CA, 1987 Suche in Google Scholar
© 2015 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
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Artikel in diesem Heft
- The M-Regular Graph of a Commutative Ring
- Further Properties of the Lattice of Torsion Classes of Abelian Cyclically Ordered Groups
- Free Power-Commutative Groupoids
- On Systems of Independent Sets
- Note on G-Module Structure of Orders
- Semisimple Hopf Algebras of Dimension 2q3
- On the Convergence of a Mapped by a Function
- Multiple Solutions of Nonlinear Fractional Differential Equations with p-Laplacian Operator and Nonlinear Boundary Conditions
- Meromorphic Functions Sharing Pairs of Small Functions
- Sharp Inequalities for Polygamma Functions
- Existence Results for Some Higher-Order Evolution Equations with Time-Dependent Unbounded Operator Coefficients
- Existence of Ground State Solutions for Hamiltonian Elliptic Systems with Gradient Terms
- Approximate Higher Ring Derivations in Non-Archimedean Banach Algebras
- Characterizations of Banach Spaces which are not Isomorphic to any of their Proper Subspaces
- Operator Inequalities Related to Q-Class Functions
- On a Class of Locally Dually Flat (α,β)–Metrics
- Limit Theorems for the Counting Function of Eigenvalues up to Edge in Covariance Matrices
- A Generalization of Jakubec's Formula