On the invertible algebras linear over an Abelian group

Journal of Contemporary Mathematical Analysis - Tập 48 - Trang 158-165 - 2013
S. S. Davidov1
1Yerevan State University, Yerevan, Armenia

Tóm tắt

In this paper using the second order formula, namely the ∀∃(∀)-identities, we characterize some subclasses of the invertible algebras that are linear over an Abelian group and have restrictions on the use of the automorphisms of the corresponding group.

Tài liệu tham khảo

V. D. Belousov, Foundations of the Ttheory of Quasigroups and Loops (Moscow, Nauka, 1967). V. D. Belousov, “Balanced identities on the quasigroups”, Math. Sb., 70(112), 55–97, 1966. T. Kepka, P. Nemec, “T-quasigroups. Part I”. Acta Universitatis Carolina Mat. et Phys., 12(1), 39–49, 1971. G. B. Belyavskaya, “T-quasigroups and the center of a quasigroup”, Mat. Issledov. Kishinev, Shtinica, 111, 24–43, 1989. G. B. Belyavskaya, A. Kh. Tabarov, “A characterization of linear and alinear quasigroups”. Discr. Mat., RAN, 4(2), 142–147, 1992. S. S. Davidov, “A characterization of binary invertible algebras linear over a group”, Quasigroups and Related Systems, 19, 207–222, 2011. Yu.M. Movsisyan, E. Nazari, “Transitive modes”, Demonstratio Mathematica, 44(3), 511–522, 2011. T. Kepka, “Structure of weakly abelian quasigroups”, Czech Math. Journal, 28, 181–188, 1978. T. Kepka, “Structure of triabelian quasigroups”, Comment. Math.Univ. Caroline., 17, 229–240, 1976. A. P. Keedwell, V. A. Shcherbacov, “Quasigroups with an inverse property and generalized parastrophic identities”, Quasigruops and Related Systems, 13, 109–124, 2005. J. Cho, J. Ježek, T. Kepka, “Paramedial groupoids”, Czech.Math. Journal, 49(124), 277–290, 1999. A. Kh. Tabarov, “T-algebras with additional identities”. Dep. in VINITI, Moscow, 09.01.91, N163-B91, 1991. A. Kh. Tabarov, “On some varieties of the Abelian quasigroups”, Discr. Mat., RAN, 12(3), 154–159, 2000. V. D. Belousov, “Parastrophic-orthogonal quasigroups”, Preprint AN MSSR, Inst. Mat. Kishinev, 1983.