Structure theorems for idempotent residuated lattices
نویسندگان
چکیده
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 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 کاملThe Structure of Residuated Lattices
A residuated lattice is an ordered algebraic structure L = 〈L,∧,∨, · , e, \ , / 〉 such that 〈L,∧,∨〉 is a lattice, 〈L, ·, e〉 is a monoid, and \ and / are binary operations for which the equivalences a · b ≤ c ⇐⇒ a ≤ c/b ⇐⇒ b ≤ a\c hold for all a, b, c ∈ L. It is helpful to think of the last two operations as left and right division and thus the equivalences can be seen as “dividing” on the right...
متن کاملTopological Residuated Lattices
In this paper, we study the separtion axioms $T_0,T_1,T_2$ and $T_{5/2}$ on topological and semitopological residuated lattices and we show that they are equivalent on topological residuated lattices. Then we prove that for every infinite cardinal number $alpha$, there exists at least one nontrivial Hausdorff topological residuated lattice of cardinality $alpha$. In the follows, we obtain some ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebra universalis
سال: 2020
ISSN: 0002-5240,1420-8911
DOI: 10.1007/s00012-020-00659-5