Residuated lattice of L-fuzzy ideals of a ring

Foka, S. V. Tchoffo; Tonga, Marcel

doi:10.1007/s00500-020-04894-9

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2021

2023

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“…Almost all aspects of classical algebraic structures are "fuzzified". Besides fuzzy groups, which were studied by hundreds of investigators (e.g., [2][3][4][5][6]), various aspects of fuzzy rings are also investigated (e.g., [7][8][9][10][11]).…”

Section: Introductionmentioning

confidence: 99%

Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields

Jimenez,

Serrano,

Šešelja

et al. 2023

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Omega rings (Ω-rings) (and other related structures) are lattice-valued structures (with Ω being the codomain lattice) defined on crisp algebras of the same type, with lattice-valued equality replacing the classical one. In this paper, Ω-ideals are introduced, and natural connections with Ω-congruences and homomorphisms are established. As an application, a framework of approximate solutions of systems of linear equations over Ω-fields is developed.

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