• 제목/요약/키워드: ordered semiring

검색결과 8건 처리시간 0.016초

A NOTE ON DERIVATIONS OF ORDERED 𝚪-SEMIRINGS

  • Kim, Kyung Ho
    • Korean Journal of Mathematics
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    • 제27권3호
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    • pp.779-791
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    • 2019
  • In this paper, we consider derivation of an ordered ${\Gamma}$-semiring and introduce the notion of reverse derivation on ordered ${\Gamma}$-semiring. Also, we obtain some interesting related properties. Let I be a nonzero ideal of prime ordered ${\Gamma}$-semiring M and let d be a nonzero derivation of M. If ${\Gamma}$-semiring M is negatively ordered, then d is nonzero on I.

CHARACTERIZATIONS OF ORDERED INTRA k-REGULAR SEMIRINGS BY ORDERED k-IDEALS

  • Ayutthaya, Pakorn Palakawong na;Pibaljommee, Bundit
    • 대한수학회논문집
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    • 제33권1호
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    • pp.1-12
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    • 2018
  • We introduce the notion of ordered intra k-regular semirings, characterize them using their ordered k-ideals and prove that an ordered semiring S is both ordered k-regular and ordered intra k-regular if and only if every ordered quasi k-ideal or every ordered k-bi-ideal of S is ordered k-idempotent.

Purities of Ordered Ideals of Ordered Semirings

  • Ayutthaya, Pakorn Palakawong na;Pibaljommee, Bundit
    • Kyungpook Mathematical Journal
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    • 제60권3호
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    • pp.455-465
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    • 2020
  • We introduce the concepts of the left purity, right purity, quasi-purity, bipurity, left weak purity and right weak purity of ordered ideals of ordered semirings and use them to characterize regular ordered semirings, left weakly regular ordered semirings, right weakly regular ordered semirings and fully idempotent ordered semirings.

A CHARACTERIZATION OF FINITE FACTORIZATION POSITIVE MONOIDS

  • Polo, Harold
    • 대한수학회논문집
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    • 제37권3호
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    • pp.669-679
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    • 2022
  • We provide a characterization of the positive monoids (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating sets satisfy the finite factorization property, while positive monoids with co-well-ordered generating sets satisfy this property if and only if they satisfy the bounded factorization property.

Valuations on Ternary Semirings

  • Pal, Sumana;Sircar, Jayasri;Mondal, Pinki
    • Kyungpook Mathematical Journal
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    • 제62권1호
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    • pp.57-67
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    • 2022
  • In the present study, we introduce a valuation of ternary semiring on an ordered abelian group. Motivated by the construction of valuation rings, we study some properties of ideals in ternary semiring arising in connection with the valuation map. We also explore ternary valuation semirings for a noncommuative ternary division semiring. We further consider the notion of convexity in a ternary semiring and how it is reflected in the valuation map.

EXTREME PRESERVERS OF TERM RANK INEQUALITIES OVER NONBINARY BOOLEAN SEMIRING

  • Beasley, LeRoy B.;Heo, Seong-Hee;Song, Seok-Zun
    • 대한수학회지
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    • 제51권1호
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    • pp.113-123
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    • 2014
  • The term rank of a matrix A over a semiring $\mathcal{S}$ is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we characterize linear operators that preserve the sets of matrix ordered pairs which satisfy extremal properties with respect to term rank inequalities of matrices over nonbinary Boolean semirings.

LINEAR PRESERVERS OF SPANNING COLUMN RANK OF MATRIX PRODUCTS OVER SEMIRINGS

  • Song, Seok-Zun;Cheon, Gi-Sang;Jun, Young-Bae
    • 대한수학회지
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    • 제45권4호
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    • pp.1043-1056
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    • 2008
  • The spanning column rank of an $m{\times}n$ matrix A over a semiring is the minimal number of columns that span all columns of A. We characterize linear operators that preserve the sets of matrix ordered pairs which satisfy multiplicative properties with respect to spanning column rank of matrices over semirings.

One-sided Prime Ideals in Semirings

  • Shabir, Muhammad;Iqbal, Muhammad Sohail
    • Kyungpook Mathematical Journal
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    • 제47권4호
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    • pp.473-480
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    • 2007
  • In this paper we define prime right ideals of semirings and prove that if every right ideal of a semiring R is prime then R is weakly regular. We also prove that if the set of right ideals of R is totally ordered then every right ideal of R is prime if and only if R is right weakly regular. Moreover in this paper we also define prime subsemimodule (generalizing the concept of prime right ideals) of an R-semimodule. We prove that if a subsemimodule K of an R-semimodule M is prime then $A_K(M)$ is also a prime ideal of R.

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