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- W2888945521 abstract "Abstract On a general hyperring, there is a fundamental relation, denoted γ * , such that the quotient set is a classical ring. In a previous paper, the authors defined the relation ε m on general hyperrings, proving that its transitive closure <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mtable> <m:mtr> <m:mtd> <m:mstyle> <m:msubsup> <m:mi>ε</m:mi> <m:mrow> <m:mi>m</m:mi> </m:mrow> <m:mrow> <m:mo>∗</m:mo> </m:mrow> </m:msubsup> </m:mstyle> </m:mtd> </m:mtr> </m:mtable> </m:math> $begin{array}{} displaystyle varepsilon^{*}_{m} end{array}$ is a strongly regular equivalence relation smaller than the γ * -relation on some classes of hyperrings, such that the associated quotient structure modulo <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mtable> <m:mtr> <m:mtd> <m:mstyle> <m:msubsup> <m:mi>ε</m:mi> <m:mrow> <m:mi>m</m:mi> </m:mrow> <m:mrow> <m:mo>∗</m:mo> </m:mrow> </m:msubsup> </m:mstyle> </m:mtd> </m:mtr> </m:mtable> </m:math> $begin{array}{} displaystyle varepsilon^{*}_{m} end{array}$ is an ordinary ring. Thus, on such hyperrings, <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mtable> <m:mtr> <m:mtd> <m:mstyle> <m:msubsup> <m:mi>ε</m:mi> <m:mrow> <m:mi>m</m:mi> </m:mrow> <m:mrow> <m:mo>∗</m:mo> </m:mrow> </m:msubsup> </m:mstyle> </m:mtd> </m:mtr> </m:mtable> </m:math> $begin{array}{} displaystyle varepsilon^{*}_{m} end{array}$ is a fundamental relation. In this paper, we discuss the transitivity conditions of the ε m -relation on hyperrings and m -idempotent hyperrings." @default.
- W2888945521 created "2018-09-07" @default.
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- W2888945521 date "2018-01-01" @default.
- W2888945521 modified "2023-10-14" @default.
- W2888945521 title "Transitivity of the εm -relation on (m-idempotent) hyperrings" @default.
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- W2888945521 doi "https://doi.org/10.1515/math-2018-0085" @default.
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