
Summary: The main result of this paper is the introduction of the notion of 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. Some remarkable examples are added.
homomorphism, bimodule, two-sided ideal, module, one-sided ideal, Orthogonal arrays, Latin squares, Room squares, Associative rings and algebras arising under various constructions, ring with identity
homomorphism, bimodule, two-sided ideal, module, one-sided ideal, Orthogonal arrays, Latin squares, Room squares, Associative rings and algebras arising under various constructions, ring with identity
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