6533b7dcfe1ef96bd1273503
RESEARCH PRODUCT
The diamond partial order in rings
Pedro PatrícioLeila LebtahiNéstor Thomesubject
Pure mathematics15A09Principal ideal010103 numerical & computational mathematicsengineering.material01 natural sciencesCombinatoricsMatrix (mathematics)Linear extensionPrincipal ideal0101 mathematicsCiências Naturais::MatemáticasMathematicsRing (mathematics)RingAlgebra and Number TheoryScience & Technology010102 general mathematicsAnells (Algebra)DiamondOrder (ring theory)Sharp partial orderStar partial orderMinus partial order06A06Linear algebraengineeringÀlgebra linealMATEMATICA APLICADAMaximal element:Matemáticas [Ciências Naturais]description
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 analyze successors, predecessors and maximal elements under the diamond order.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-03-26 |