Coproducts of Bounded Distributive Lattices

نویسنده

  • Jonathan David Farley
چکیده

Let LM denote the coproduct of the bounded distributive lattices L and M. At the 1981 Bann Conference on Ordered Sets, the following question was posed: What is the largest class L of nite distributive lattices such that, for every non-trivial Boolean lattice B and every L 2 L, B L = B L 0 implies L = L 0 ? In this note, the problem is solved.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Coproducts of bounded distributive lattices: cancellation

Let L ∗ M denote the coproduct of the bounded distributive lattices L and M . At the 1981 Banff Conference on Ordered Sets, the following question was posed: What is the largest class L of finite distributive lattices such that, for every non-trivial Boolean lattice B and every L ∈ L, B ∗ L = B ∗ L′ implies L = L′? In this note, the problem is solved.

متن کامل

Distributive lattices with strong endomorphism kernel property as direct sums

Unbounded distributive lattices which have strong endomorphism kernel property (SEKP) introduced by Blyth and Silva in [3] were fully characterized in [11] using Priestley duality (see Theorem  2.8}). We shall determine the structure of special elements (which are introduced after  Theorem 2.8 under the name strong elements) and show that these lattices can be considered as a direct product of ...

متن کامل

Coproducts of Distributive Lattice based Algebras

The analysis of coproducts in varieties of algebras has generally been variety-specific, relying on tools tailored to particular classes of algebras. A recurring theme, however, is the use of a categorical duality. Among the dualities and topological representations in the literature, natural dualities are particularly well behaved with respect to coproduct. Since (multisorted) natural dualitie...

متن کامل

Configurations in Coproducts of Priestley Spaces

Let P be a configuration, i.e., a finite poset with top element. Let Forb(P ) be the class of bounded distributive lattices L whose Priestley space P(L) contains no copy of P . We show that the following are equivalent: Forb(P ) is first-order definable, i.e., there is a set of first-order sentences in the language of bounded lattice theory whose satisfaction characterizes membership in Forb(P ...

متن کامل

Profinite Heyting Algebras and Profinite Completions of Heyting Algebras

This paper surveys recent developments in the theory of profinite Heyting algebras (resp. bounded distributive lattices, Boolean algebras) and profinite completions of Heyting algebras (resp. bounded distributive lattices, Boolean algebras). The new contributions include a necessary and sufficient condition for a profinite Heyting algebra (resp. bounded distributive lattice) to be isomorphic to...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1999