MATHEMATICA BOHEMICA, Vol. 136, No. 1, pp. 91-103, 2011

On algebras of generalized Latin squares

František Katrnoška

František Katrnoška, Department of Mathematics, Institute of Chemical Technology, Technická 5, 166 28 Praha 6, Czech Republic

Abstract: The main result of this paper is the introduction of a notion of a generalized $R$-Latin square, which includes as a special case the standard Latin square, as well as the magic square, and also the double stochastic matrix. Further, the algebra of all generalized Latin squares over a commutative ring with identity is investigated. Moreover, some remarkable examples are added.

Keywords: ring with identity, homomorphism, one-sided ideal, two-sided ideal, module, bimodule

Classification (MSC 2010): 05B15, 16S99

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