The goal of this paper is study closed ideals and annihilators over the class distributive dual weakly complemented lattices(DDWCL's). algebraic structure ideals, dense are shown. connection between andannihilators in obtained.

An n-ary operation Q : Σ → Σ is called an n-ary quasigroup of order |Σ| if in the equation x0 = Q(x1, . . . , xn) knowledge of any n elements of x0, . . . , xn uniquely specifies the remaining one. An n-ary quasigroup Q is (permutably) reducible if Q(x1, . . . , xn) = P ( R(xσ(1), . . . , xσ(k)), xσ(k+1), . . . , xσ(n) ) where P and R are (n−k+1)-ary and k-ary quasigroups, σ is a permutation, a...

It is well known that a commutative ring R is complemented (that is, given a ∈ R there exists b ∈ R such that ab = 0 and a + b is a regular element) if an only if the total ring of quotients of R is von Neumann regular. We consider generalizations of the notion of a complemented ring and their implications for the total ring of quotients. We then look at the specific case when the ring is a rin...

1. Laboratory of Medical Molecular Virology, School of Medicine, Nankai University, Tianjin, Tianjin 6 300071, P.R.China. 7 2. State Key Laboratory of Veterinary Etiological Biology and Key Laboratory of Veterinary Parasitology of 8 Gansu Province, Lanzhou Veterinary Research Institute, Chinese Academy of Agricultural Science, 9 Lanzhou, Gansu 730046, P.R.China. 10 3. Co-innovation Center for P...

We prove how any (elementary) topos may be reconstructed from the data of two complemented subtoposes together with a pair of left exact \glueing func-tors". This generalizes the classical glueing theorem for toposes, which deals with the special case of an open subtopos and its closed complement. Our glueing analysis applies in a particularly simple form to a locally closed subtopos and its co...

α is a regular cardinal number or the symbol ∞, and X is a compact Hausdorff space. It is shown that (Theorem 2.1) X is αcozerocomplemented iff each αBorel set differs from an αcozero set by a meagre set. This immediately yields (Corollary 2.2) X is αdisconnected iff each αBorel set differs from a clopen set by a meagre set. (The cases α = ∞ in Theorem 2.1, and α = ω1 in Corollary 2.2 are impor...

It is shown that the span of fa i h i b i e i g n i=1 , where fh i g is the Haar system in L p and fe i g the canonical basis of`p , is well isomorphic to a well complemented subspace of L p ; 2 < p < 1. As a consequence we get that there is a rearrangement of the (initial segments of the) Haar system in L p ; 2 < p < 1, any block basis of which is well isomorphic to a well complemented subspac...

In 1962, the authors proved that every finite distributive lattice can be represented as the congruence lattice of a finite sectionally complemented lattice. In 1992, M. Tischendorf verified that every finite lattice has a congruence-preserving extension to an atomistic lattice. In this paper, we bring these two results together. We prove that every finite lattice has a congruence-preserving ex...