Browsing by Author "Ceban, Dina"

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Asupra p -quasigrupurilor de tipul T2 [Articol]
(CEP USM, 2014) Ceban, Dina
ASUPRA π-T-QUASIGRUPURILOR
(CEP USM, 2013-09-26) Ceban, Dina
ON ORTHOGONAL SYSTEMS OF TERNARY QUASIGROUPS ADMITTING NONTRIVIAL PARATOPIES.
(Institutul de Matematică şi Informatică al AŞM, 2017) Syrbu, Parascovia; Ceban, Dina
In the present workwe describ eallorthogonal systems consisting of three ternary quasigroupop erations and of all (three) ternary selectors,admitting at least one nontrivial paratopy. In[11]we proved that there exist precisely 48 orthogonal systems of the considered form,admitting atleast one paratopy,which components are three quasigroupop erations,or two quasigroupop erations and a selector. Now we show that there exist precisely 105 such systems, admitting at least one nontrivial paratopy which comp onents are two selectors and a quasigroup op eration, or three selectors.
ON QUASIGROUPS WITH SOME MINIMAL IDENTITIES
(CEP USM, 2015) Ceban, Dina; Syrbu, Parascovia
Quasigroups with two identities (of typesT1 and T2) from Belousov-Bennett classification are considered. It is proved that a π-quasigroup of type T2 is also of type only if it satisfies the identity yx∙x=y (the “right keys law”), so π -quasigroups that are of both types T1and T2 are RIP - quasigroups. Also, it is proved that π-quasigroups of type T2 are isotopic to idempotent quasigroups. Necessary and sufficient conditions when a π -quasigroup of typeT2 is isotopic to a group (an abelian group) are found. It is shown that the set of all π-quasigroups of type T2 isotopic to abelian groups is a subvariety in the variety of all π -quasigroups of type T2 and that π- T-quasigroups of type T2 are medial quasigroups. Using the symmetric group on Q∙Q, some considerations for the spectrum of finite π-quasigroups (Q1) of type T1 are discussed.
ON SOME IDENTITIES IN TERNARY QUASIGROUPS
(CEP USM, 2016) Ceban, Dina
Identities of length 5, with two variables in binary quasigroups are called minimal identities. V.Belousov and, independently, F. Bennett showed that, up to the parastrophic equivalence, there are seven minimal identities. The existence of paratopiesof orthogonal systems,consistingof two binary quasigroups and the binary selectors,implies three minimal identities (of seven).The existence of paratopies of orthogonal system, consisting of three ternary quasigroups and the ternary selectors, gives 67 identities. In the present article these identities are listed and it is proved that each of 67 identities is equivalentto one of the following four identities: α A ( β A, γ A,δ A)= E1, α A ( β A, γ A,E1) = E2, : α A (β A, E1, E2) = , γ A (β A, E1, E3), α A ( β A, E1, E2 ) = γ A (β A, E1 E2) , where A is a ternary quasigroup and ÷α,β,γ,δ∈〖S4〗_ necessary condition when a tuple θ = ( A1 ,A, 2, …,A n ) consisting of n-ary quasigroups, defined on a set Q2 Место для формулы., is a paratopy of the orthogonal system ∑{ A1, A2, …, An, E1, E2, …, En} is given
ON THE HOLOMORPH OF ¼-QUASIGROUPS OF TYPE T1
("VALINEX", 2014) Ceban, Dina; Syrbu, Parascovia
Quasigroups satisfying the identity x¢(x¢(x¢y)) = y are called ¼-quasigroups of type T1. Necessary and su±cient conditions for the holomorph of a ¼-quasigroup of type T1 to be a ¼-quasigroup of type T1 are established. Also, it is proved that the left (right) multiplication group of a ¼-quasigroup of type T1 is isomorphic to some normal subgroup of the left (right) multiplication group of its holomorph, respectively.
ON Π-QUASIGROUPS OF TYPET1
(Academy of Sciences of Moldova, 2014) Syrbu, Parascovia; Ceban, Dina
Quasigroups satisfying the identityx(x· xy ) = y are called π -quasigroups of type T 1 . The spectrum of the defining identity is precisely q = 0 or 1(mod 3), except for q = 6. Necessary conditions when a finite π -quasigroup of type T 1 has the order q = 0 (mod 3), are given. In particular, it is proved that a finite π -quasigroup of type T 1 such that the order of its inner mapping group is not divisible by three has a left unit. Necessary and sufficient conditions when the identityx ( x · xy ) = y is invariant under the isotopy of quasigroups (loops) are found