منابع مشابه
Congruence semimodular varieties I: Locally finite varieties
The lattice of closed subsets of a set under such a closure operator is semimodular. Perhaps the best known example of a closure operator satisfying the exchange principle is the closure operator on a vector space W where for X ___ W we let C(X) equal the span of X. The lattice of C-closed subsets of W is isomorphic to Con(W) in a natural way; indeed, if Y _~ W x W and Cg(Y) denotes the congrue...
متن کاملA Characterization of Decidable Locally Finite Varieties
We describe the structure of those locally finite varieties whose first order theory is decidable. A variety is a class of universal algebras defined by a set of equations. Such a class is said to be locally finite if every finitely generated member of the class is finite. It turns out that in order for such a variety to have a decidable theory it must decompose into the varietal product of thr...
متن کاملA Characterization of Minimal Locally Finite Varieties
In this paper we describe a one–variable Mal′cev–like condition satisfied by any locally finite minimal variety. We prove that a locally finite variety is minimal if and only if it satisfies this Mal′cev–like condition and it is generated by a strictly simple algebra which is nonabelian or has a trivial subalgebra. Our arguments show that the strictly simple generator of a minimal locally finit...
متن کاملLocally finite varieties of Heyting algebras
We show that for a variety V of Heyting algebras the following conditions are equivalent: (1) V is locally finite; (2) the V-coproduct of any two finite V-algebras is finite; (3) either V coincides with the variety of Boolean algebras or finite V-copowers of the three element chain 3 ∈ V are finite. We also show that a variety V of Heyting algebras is generated by its finite members if, and onl...
متن کاملFiniteness Properties of Locally Finite Abelian Varieties
We show that any locally finite abelian variety is generated by a finite algebra. We solve a problem posed by D. Hobby and R. McKenzie by exhibiting a nonfinitely based finite abelian algebra.
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: Bulletin of the Australian Mathematical Society
سال: 1976
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700024850