A sheaf representation of distributive pseudocomplemented lattices

Cornish, William H.

doi:10.1090/S0002-9939-1976-0424630-2

A sheaf representation of distributive pseudocomplemented lattices
HTML articles powered by AMS MathViewer

by William H. Cornish PDF

Proc. Amer. Math. Soc. 57 (1976), 11-15 Request permission

Abstract:

The main result of this paper shows that a distributive pseudocomplemented lattice $(L; \vee , \wedge {,^ \ast },0,1)$, considered as an algebra of type $\langle 2,2,1,0,0\rangle$, can be represented as the algebra of all global sections in a certain sheaf. The stalks are the quotient algebras $L/\Theta (O(P))$, where $P$ is a prime ideal in $L$. The base space is the set of prime ideals of $L$ equipped with the topology whose basic open sets are of the form $P:P$ prime in $L,{x^{ \ast \ast }} \notin P$ for some $x \in L$.

References

William H. Cornish, Annulets and $\alpha$-ideals in a distributive lattice, J. Austral. Math. Soc. 15 (1973), 70–77. MR 0344170
William H. Cornish, Congruences on distributive pseudocomplemented lattices, Bull. Austral. Math. Soc. 8 (1973), 161–179. MR 318024, DOI 10.1017/S0004972700042404
William H. Cornish, $n$-normal lattices, Proc. Amer. Math. Soc. 45 (1974), 48–54. MR 340133, DOI 10.1090/S0002-9939-1974-0340133-6

On the Chinese remainder theorem of H. Draškovičová

Brian A. Davey, Sheaf spaces and sheaves of universal algebras, Math. Z. 134 (1973), 275–290. MR 330006, DOI 10.1007/BF01214692
Patrick N. Stewart, A sheaf theoretic representation of rings with Boolean orthogonalities, Pacific J. Math. 58 (1975), no. 1, 249–254. MR 376776