منابع مشابه
Commutative Idempotent Residuated Lattices
We investigate the variety of residuated lattices with a commutative and idempotent monoid reduct. A residuated lattice is an algebra A = (A,∨,∧, ·, e, /, \) such that (A,∨,∧) is a lattice, (A, ·, e) is a monoid and for every a, b, c ∈ A ab ≤ c ⇔ a ≤ c/b ⇔ b ≤ a\c. The last condition is equivalent to the fact that (A,∨,∧, ·, e) is a lattice-ordered monoid and for every a, b ∈ A there is a great...
متن کاملRepresentable Idempotent Commutative Residuated Lattices
It is proved that the variety of representable idempotent commutative residuated lattices is locally finite. The n-generated subdirectly irreducible algebras in this variety are shown to have at most 3n+1 elements each. A constructive characterization of the subdirectly irreducible algebras is provided, with some applications. The main result implies that every finitely based extension of posit...
متن کاملSpectral Lattices of Reducible Matrices over Completed Idempotent Semifields
Previous work has shown a relation between L-valued extensions of FCA and the spectra of some matrices related to L-valued contexts. We investigate the spectra of reducible matrices over completed idempotent semifields in the framework of dioids, naturally-ordered semirings, that encompass several of those extensions. Considering special sets of eigenvectors also brings out complete lattices in...
متن کاملCayley’s and Holland’s Theorems for Idempotent Semirings and Their Applications to Residuated Lattices
We extend Cayley’s and Holland’s representation theorems to idempotent semirings and residuated lattices, and provide both functional and relational versions. Our analysis allows for extensions of the results to situations where conditions are imposed on the order relation of the representing structures. Moreover, we give a new proof of the finite embeddability property for the variety of integ...
متن کاملNoether Normalisation
Proof. Let A = k[s1, . . . , sn] where s1, . . . , sn ∈ A. We assume that A is not integral over k, in which case at least one of the si is not algebraic over k. If the set {s1, . . . , sn} is algebraically independent, then we are done. Otherwise assume that sn is algebraic over k[s1, . . . , sn−1] (by relabeling if necessary). Let f(x1, . . . , xn) be a nonzero polynomial with f(s1, . . . , s...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1969
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1969-0241326-7