Connections between commutative rings and some algebras of logic
محل انتشار: مجله سیستم های فازی، دوره: 19، شماره: 6
سال انتشار: 1401
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 210
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شناسه ملی سند علمی:
JR_IJFS-19-6_008
تاریخ نمایه سازی: 17 آبان 1401
چکیده مقاله:
In this paper using the connections between some subvarieties of residuatedlattices, we investigated some properties of the lattice of ideals incommutative and unitary rings. We give new characterizations for commutativerings A in which Id(A) is an MV-algebra, a Heyting algebra or a Booleanalgebra and we establish connections between these types of rings. We arevery interested in the finite case and we present summarizing statistics. Weshow that the lattice of ideals in a finite commutative ring is a Booleanalgebra or an MV-algebra (which is not Boolean).Using this result we generate the binary block codes associated to thelattice of ideals in finite commutative rings and we present a new way togenerate all (up to an isomorphism) finite MV-algebras using rings.
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