Faculty of Natural Sciences and Mathematics
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Item type:Publication, The names of foreign mathematicians in Macedonian(Union of Mathematicians of Macedonia, 2016) - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Mathematical terminology: On the names of fractions in the Macedonian language(Union of Mathematicians of Macedonia, 2016) - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Ternary groupoid powers(Union of Mathematicians of Macedonia, 2009)Celakoska-Jordanova, VesnaThe notion of ternary groupoid powers is introduced and some of its properties are investigated. In particular, it is shown that the set E of ternary groupoid powers, under a suitably defined binary operation, is a cancellative monoid and that this monoid is free over the set of its irreducible elements. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Monoids of powers in varieties of f-idempotent groupoids(Hikari, Ltd., 2013)Celakoska-Jordanova, VesnaThe monoids of powers in varieties of f-idempotent groupoids and commutative f-idempotent groupoids, where f is an irreducible groupoid power with a length at least 3, are constructed. It is shown that these monoids are free over a countable set of irreducible groupoid powers. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, On quaternary associative operations(Faculty of Technical Sciences Čačak, University of Kragujevac, 2007)Celakoska-Jordanova, VesnaSome properties of quaternary associative operations that have neutral sequences are investigated. A characterization of such operations by means of binary primitive operations is established. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Free objects in the variety of groupoids defined by the identity xf(x) = f(f(x))(Hikari, Ltd., 2012)Celakoska-Jordanova, VesnaLet V_f denote the variety of groupoids defined by the identity xf(x) = f(f(x)), where f is a fixed nontrivial groupoid power. A description of free objects in this variety and their characterization by means of injective groupoids in V_f are obtained. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Free groupoids with x^{2}x^{2}=x^{3}x^{3}(Faculty of Natural Sciences and Mathematics, Skopje, 2004)Celakoska-Jordanova, VesnaA description of free objects in the variety V of groupoids defined by the identity x^{2}x^{2}=x^{3}x^{3} is obtained. The following method is used: one of the sides of the identity is considered as "suitable" and the other as "unsuitable" one. First, the left-hand side x^{2}x^{2}is chosen as "suitable" and the set of elements of F (F being an absolutely free groupoid with a basis B) containing no parts that have the form x^{3}x^{3} is taken as a "candidate" for the carrier of the desired free object in V. Continuing this procedure, a V-free object is obtained. Another construction of V-free object is obtained by choosing the right-hand side x^{3}x^{3} as "suitable" one. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Free groupoids in the class of power left and right idempotent groupoids(Hikari, Ltd., 2008)Celakoska-Jordanova, VesnaThe subject of this paper is the class of groupoids such that any groupoid G = (G, ·) of this class has the property: every subgroupoid of G generated by any element a ∈ G satisfies the identity (xx)(yy) = xy. It is shown that this class is a variety. A construction and a characterization of free groupoids in this variety are obtained. The word problem is solvable for this variety. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Canonical Objects in Classes of (n, V)-Groupoids(Bulgarian Academy of Sciences - National Committee for Mathematics, 2010)Celakoska-Jordanova, VesnaFree algebras are very important in studying classes of algebras, especially varieties of algebras. Any algebra that belongs to a given variety of algebras can be characterized as a homomorphic image of a free algebra of that variety. Describing free algebras is an important task that can be quite complicated, since there is no general method to resolve this problem. The aim of this work is to investigate classes of groupoids, i.e. algebras with one binary operation, that satisfy certain identities or other conditions, and look for free objects in such classes. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Canonical biassociative groupoids(Mathematical Institute of the Serbian Academy of Sciences and Arts, 2007)