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Invertibility of matrices over ordered algebraic systems. (English. Russian original) Zbl 0906.15002

Sib. Math. J. 39, No. 3, 476-483 (1998); translation from Sib. Mat. Zh. 39, No. 3, 551-559 (1998).
L. A. Skornyakov [Sib. Mat. Zh. 27, No. 2(156), 182-185 (1986; Zbl 0595.15003)] gave a description of invertible matrices over distributive lattices. The author generalizes it to the case of ordered algebraic systems (of ordered groupoids with an upper semilattice structure on them). The systems were considered by T. S. Blyth [J. Lond. Math. Soc., III Ser. 39, 427-432 (1964; Zbl 0154.01104)], whose results appear as immediate corollaries of the results presented in the article under review.

MSC:

15A09 Theory of matrix inversion and generalized inverses
06F05 Ordered semigroups and monoids
06F25 Ordered rings, algebras, modules
15A30 Algebraic systems of matrices
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