Lecture Notes on Algebraic Structure of Lattice-Ordered Rings

Ma, Jingjing

doi:10.1142/9009

Cited by 19 publications

(3 citation statements)

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“…It is also partially ordered set but it is not totally ordered set since there exists (1,4) and (2,3) on R R  that is not satisfies whether (1,4) ≤ (2,3) or (1,4)…”

Section: Posetmentioning

confidence: 99%

Partially Ordered Group of the 2×2 Symmetric Matrices

Hasanah

2019

InPrime:Ind.Jour.Pure.Applied.Math

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This paper deals with the partially ordered group of the 2×2 symmetric matrices. A matrix is defined to be a positive if each entry of the matrix is positive. With the characterization of the 2×2 symmetric matrix, we construct the positive cone such that the set of the matrices constructs partially ordered group.Keywords: Symmetric Matrix, Group-Ordered, Positive Cone. AbstrakArtikel ini membahas grup terurut parsial pada matriks simetri berukuran 2×2. Suatu matriks dikatakan positif jika setiap entri pada matriks bernilai positif. Melalui karakteristik dari matriks simetri, akan dikonstruksi sebuah positif cone sehingga matriks simetri berukuran 2×2 merupakan grup terurut parsial.Kata kunci: Matriks Simetri, Grup Terurut, Positif Cone.

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“…It is also partially ordered set but it is not totally ordered set since there exists (1,4) and (2,3) on R R  that is not satisfies whether (1,4) ≤ (2,3) or (1,4)…”

Section: Posetmentioning

confidence: 99%

Partially Ordered Group of the 2×2 Symmetric Matrices

Hasanah

2019

InPrime:Ind.Jour.Pure.Applied.Math

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“…By [3,Theorem 4.33], C cannot be made into an -algebra over D which is algebraic over f (C) since in this case, the lattice order on C can be extended to its quotient field F + F i, which is not possible by Theorem 4.…”

Section: Examplementioning

confidence: 99%

“…A po-algebra R is called a directed algebra if the partial order is a directed partial order, that is, any element in R is a difference of two positive elements; and a po-algebra R is called a lattice-ordered algebra ( -algebra) if the partial order is a lattice order. In this article, we study partial orders on C and H to make them into a po-algebra over D. For undefined terminologies and background information on po-rings and -rings, the reader is referred to [1,2,3].…”

Section: Introductionmentioning

confidence: 99%