Local polynomial functions on lattices and universal algebras
نویسندگان
چکیده
منابع مشابه
On residuated lattices with universal quantifiers
We consider properties of residuated lattices with universal quantifier and show that, for a residuated lattice $X$, $(X, forall)$ is a residuated lattice with a quantifier if and only if there is an $m$-relatively complete substructure of $X$. We also show that, for a strong residuated lattice $X$, $bigcap {P_{lambda} ,|,P_{lambda} {rm is an} m{rm -filter} } = {1}$ and hence that any strong re...
متن کاملAn equivalence functor between local vector lattices and vector lattices
We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-...
متن کاملPseudo-polynomial Functions over Finite Distributive Lattices
In this paper we extend the authors’ previous works [6, 7] by considering an aggregation model f : X1 × · · · × Xn → Y for arbitrary sets X1, . . . ,Xn and a finite distributive lattice Y , factorizable as f(x1, . . . , xn) = p(φ1(x1), . . . , φn(xn)), where p is an n-variable lattice polynomial function over Y , and each φk is a map from Xk to Y . Following the terminology of [6, 7], these are...
متن کاملQuasi-polynomial Functions over Bounded Distributive Lattices
In [6] the authors introduced the notion of quasi-polynomial function as being a mapping f : Xn → X defined and valued on a bounded chain X and which can be factorized as f(x1, . . . , xn) = p(φ(x1), . . . , φ(xn)), where p is a polynomial function (i.e., a combination of variables and constants using the chain operations ∧ and ∨) and φ is an order-preserving map. In the current paper we study ...
متن کاملAssociative Polynomial Functions over Bounded Distributive Lattices
The associativity property, usually defined for binary functions, can be generalized to functions of higher arities as well as to functions of multiple arities. In this paper, we investigate these two generalizations in the case of polynomial functions over bounded distributive lattices and present explicit descriptions of the corresponding associative functions. We also show that, in this case...
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: Colloquium Mathematicum
سال: 1979
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-42-1-83-93