Generators of lattice varieties
نویسنده
چکیده
Although it is well known that the variety of all lattices is generated by the subclass of finite lattices, there are lattice varieties which are not generated by their finite members . In fact, there are modular varieties which are not even generated by their finite dimensional members [3]. At the present t ime it is not known if the variety of all modular lattices is generated by its finite or even its finite dimensional members . This raises the question: Do there exist generators for lattice varieties which satisfy some kind of finiteness conditions? In this note we will be concerned with generators satisfying atomicity conditions. Since any lattice variety is generated by its subdirectly irreducible members , we shall be particularly interested in generators which are also subdirectly irreducible. The main results are the following. The notation and terminology for this paper is taken from [1].
منابع مشابه
Gromov-witten Invariants of a Class of Toric Varieties
1.1. Background. Toric varieties admit a combinatorial description, which allows many invariants to be expressed in terms of combinatorial data. Batyrev [Ba2] and Morrison and Plesser [MP] describe the quantum cohomology rings of certain toric varieties, in terms of generators (divisors and formal q variables) and relations (linear relations and q-deformed monomial relations). The relations are...
متن کاملVarieties of Differential Modes Embeddable into Semimodules
Differential modes provide examples of modes that do not embed as subreducts into semimodules over commutative semirings. The current paper studies differential modes, so-called Szendrei differential modes, which actually do embed into semimodules. These algebras form a variety. The main result states that the lattice of non-trivial subvarieties is dually isomorphic to the (non-modular) lattice...
متن کاملMatchings in simplicial complexes, circuits and toric varieties
Using a generalized notion of matching in a simplicial complex and circuits of vector configurations, we compute lower bounds for the minimum number of generators, the binomial arithmetical rank and the A-homogeneous arithmetical rank of a lattice ideal. Prime lattice ideals are toric ideals, i.e. the defining ideals of toric varieties. © 2006 Elsevier Inc. All rights reserved.
متن کاملIdeal of Lattice homomorphisms corresponding to the products of two arbitrary lattices and the lattice [2]
Abstract. Let L and M be two finite lattices. The ideal J(L,M) is a monomial ideal in a specific polynomial ring and whose minimal monomial generators correspond to lattice homomorphisms ϕ: L→M. This ideal is called the ideal of lattice homomorphism. In this paper, we study J(L,M) in the case that L is the product of two lattices L_1 and L_2 and M is the chain [2]. We first characterize the set...
متن کاملFree Lukasiewicz and Hoop Residuation Algebras
Hoop residuation algebras are the {→, 1}-subreducts of hoops; they include Hilbert algebras and the {→, 1}-reducts of MV-algebras (also known as Wajsberg algebras). The paper investigates the structure and cardinality of finitely generated algebras in varieties of kpotent hoop residuation algebras. The assumption of k-potency guarantees local finiteness of the varieties considered. It is shown ...
متن کامل