Il’in, S. N. 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. Reviewer: A.N.Ryaskin (Novosibirsk) Cited in 1 Document MSC: 15A09 Theory of matrix inversion and generalized inverses 06F05 Ordered semigroups and monoids 06F25 Ordered rings, algebras, modules 15A30 Algebraic systems of matrices Keywords:invertible matrix; matrix over an ordered algebraic system; groupoid; upper semilattice Citations:Zbl 0595.15003; Zbl 0154.01104 PDFBibTeX XMLCite \textit{S. N. Il'in}, Sib. Math. J. 39, No. 3, 551--559 (1998; Zbl 0906.15002); translation from Sib. Mat. Zh. 39, No. 3, 551--559 (1998)