Characterization of obstinate HuMV-ideals

Bakhshi Mahmood; Radfar Akefe

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Дифференциальные, интегральные и другие функциональные уравнения. Конечные разности. Вариационное исчисление. Функциональный анализ (243)

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BAKHSHI, Mahmood, RADFAR, Akefe. Characterization of obstinate HuMV-ideals. In: Quasigroups and Related Systems, 2019, vol. 27, nr. 2(42), pp. 181-200. ISSN 1561-2848.

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Quasigroups and Related Systems

Volumul 27, Numărul 2(42) / 2019 / ISSN 1561-2848

Characterization of obstinate H_uMV-ideals

CZU: 512.563+517.98

Pag. 181-200

Bakhshi Mahmood¹, Radfar Akefe²

¹ Department of Computer Science, Kosar University of Bojnord,
² Payame Noor University

Disponibil în IBN: 9 ianuarie 2020

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One motivation to study obstinate ideals in any algebra of logic is that the induced quotient algebra by these ideals is the two-element Boolean algebra. In this paper, we introduce two types of obstinate ideals in HvMV-algebras; obstinate HvMV-ideals and obstinate weak HvMV-ideals. Giving several theorems and examples we characterize these HvMV-ideals. For example, we prove that an HvMV-ideal (if exists) must be maximal, and any HvMV-algebra with odd number of elements does not contatin an obstinate HvMV-ideal. Also, we characterize these HvMV-ideals in nite HvMV-algebras with at most six elements; we investigate that which subsets can be an obstinate (weak) HvMV-ideal. In the sequel, we investigate the relationships between obstinate (weak) HvMV-ideals, and Boolean and prime HvMV-ideals. Finally, we prove that in a commutative HvMV-algebra, the quotient HvMV-algebra induced by an obstinate weak HvMV-ideal must be a two-elements Boolean algebra.

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