To Professor ART Solarin on his 60th Birthday Celebration SOME NORMAL CONGRUENCES IN QUASIGROUPS DETERMINED BY LINEAR-BIVARIATE POLYNOMIALS OVER THE RING
نویسنده
چکیده
In this work, two normal congruences are built on two quasigroups with underlining set Zn relative to the linear-bivariate polynomial P (x, y) = a+ bx+ cy that generates a quasigroup over the ring Zn. Four quasigroups are built using the normal congruences and these are shown to be homomorphic to the quasigroups with underlining set Zn. Some subquasigroups of the quasigroups with underlining set Zn are also found. 2000 Mathematics Subject Classification: 20N02, 20N05.
منابع مشابه
Sr and Sz Algorithms for the Symplectic (butterry) Eigenproblem
SR and SZ algorithms for the symplectic (generalized) eigen-problem that are based on the reduction of a symplectic matrix to symplectic butterry form are discussed. A 2n 2n symplectic butterry matrix has 8n ? 4 (generically) nonzero entries, which are determined by 4n ? 1 parameters. While the SR algorithm operates directly on the matrix entries, the SZ algorithm works with the 4n ?1 parameter...
متن کاملSolving System of Linear Congruence Equations over some Rings by Decompositions of Modules
In this paper, we deal with solving systems of linear congruences over commutative CF-rings. More precisely, let R be a CF-ring (every finitely generated direct sum of cyclic R-modules has a canonical form) and let I_1,..., I_n be n ideals of R. We introduce congruence matrices theory techniques and exploit its application to solve the above system. Further, we investigate the application of co...
متن کاملBivariate delta-evolution equations and convolution polynomials: Computing polynomial expansions of solutions
This paper describes an application of Rota and collaborator’s ideas on the foundations on combinatorial theory to the computing of solutions of some linear functional partial differential equations. We give a dynamical interpretation of the convolution families of polynomials as the entries, in the matrix representation, of the exponentials of certain contractive linear operators in the ring o...
متن کاملProfessor Arto Urtti -A northern light from the land of the midnight sun.
Professor Arto Urtti had his 60th birthday in December 2016. He is currently the Professor of Biopharmaceutics at the University of Helsinki and University of Eastern Finland (UEF). He was the editor-in-chief of European Journal of Pharmaceutical Sciences (EJPS) in 2001–2011, and this special issue of EJPS is dedicated to Arto in honour of his 60th birthday. The celebrations include a scientifi...
متن کاملPolynomial invariants for a semisimple and cosemisimple Hopf algebra of finite dimension Dedicated to Professor Noriaki Kawanaka on the occasion of his 60th birthday
We introduce new polynomial invariants of a finite-dimensional semisimple and cosemisimple Hopf algebra A over a field k by using the braiding structures of A. We investigate basic properties of the polynomial invariants including stability under extension of the base field. Furthermore, we show that our polynomial invariants are indeed tensor invariants of the representation category of A, and...
متن کامل