On algebras of generalized Latin squares . (English) Zbl 1224.05066

Katrnoška, František

Math. Bohem. 136, No. 1, 91-103 (2011).

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.

MSC:

05B15	Orthogonal arrays, Latin squares, Room squares
16S99	Associative rings and algebras arising under various constructions

Keywords:

ring with identity; homomorphism; one-sided ideal; two-sided ideal; module; bimodule