The diamond partial order in rings

The diamond partial order in rings

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The diamond partial order in rings

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Lebtahi, Leila; Patrício, Pedro; Thome, Néstor
This document is a artículoDate2014

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In this paper we introduce a new partial order on a ring, namely the diamond partial order. This order is an extension of a partial order defined in a matrix setting in [J.K. Baksalary and J. Hauke, A further algebraic version of Cochran's theorem and matrix partial orderings, Linear Algebra and its Applications, 127, 157-169, 1990]. We characterize the diamond partial order on rings and study its relationships with other partial orders known in the literature. We also analyse successors, predecessors and maximal elements under the diamond order.

    Lebtahi, Leila Patrício, Pedro Thome, Néstor 2014 The diamond partial order in rings Linear & Multilinear Algebra 62 3 386 395

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