Formalization of Generalized Almost Distributive Lattices
نویسندگان
چکیده
منابع مشابه
Formalization of Generalized Almost Distributive Lattices
Almost Distributive Lattices (ADL) are structures defined by Swamy and Rao [11] as a common abstraction of some generalizations of the Boolean algebra. In our paper, we deal with a certain further generalization of ADLs, namely the Generalized Almost Distributive Lattices (GADL). Our main aim was to give the formal counterpart of this structure and we succeeded formalizing all items from the Se...
متن کاملGeneralized Almost Distributive Lattices-I
The concept of a GADL as a generalization of an ADL is introduced. Necessary and sufficient conditions for a GADL to become a distributive lattice and a GADL to become an ADL are obtained. We also study the maximal sets in a GADL and give equivalent conditions for a GADL to become a distributive lattice in terms of maximal
متن کاملOn Ideals and Congruences of Generalized Almost Distributive Lattices
Necessary and sufficient conditions for a GADL to become an ADL are obtained interms of congruence relations and proved that every associative GADL is an ADL.
متن کاملFinite distributive lattices are congruence lattices of almost- geometric lattices
A semimodular lattice L of finite length will be called an almost-geometric lattice, if the order J(L) of its nonzero join-irreducible elements is a cardinal sum of at most two-element chains. We prove that each finite distributive lattice is isomorphic to the lattice of congruences of a finite almost-geometric lattice.
متن کاملExtended Ideals of Almost Distributive Lattices
The concept of extended ideals in an Almost distributive Lattice is introduced and studied their properties.
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: Formalized Mathematics
سال: 2014
ISSN: 1898-9934
DOI: 10.2478/forma-2014-0026