A sheaf representation of distributive pseudocomplemented lattices

Author:
William H. Cornish

Journal:
Proc. Amer. Math. Soc. **57** (1976), 11-15

MSC:
Primary 06A23

MathSciNet review:
0424630

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Abstract: The main result of this paper shows that a distributive pseudocomplemented lattice , considered as an algebra of type , can be represented as the algebra of all global sections in a certain sheaf. The stalks are the quotient algebras , where is a prime ideal in . The base space is the set of prime ideals of equipped with the topology whose basic open sets are of the form prime in for some .

**[1]**William H. Cornish,*Annulets and 𝛼-ideals in a distributive lattice*, J. Austral. Math. Soc.**15**(1973), 70–77. MR**0344170****[2]**William H. Cornish,*Congruences on distributive pseudocomplemented lattices*, Bull. Austral. Math. Soc.**8**(1973), 161–179. MR**0318024****[3]**William H. Cornish,*𝑛-normal lattices*, Proc. Amer. Math. Soc.**45**(1974), 48–54. MR**0340133**, 10.1090/S0002-9939-1974-0340133-6**[4]**-,*On the Chinese remainder theorem of H. Draškovičová*, Mat. Časopis (submitted).**[5]**Brian A. Davey,*Sheaf spaces and sheaves of universal algebras*, Math. Z.**134**(1973), 275–290. MR**0330006****[6]**Patrick N. Stewart,*A sheaf theoretic representation of rings with Boolean orthogonalities*, Pacific J. Math.**58**(1975), no. 1, 249–254. MR**0376776**

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DOI:
https://doi.org/10.1090/S0002-9939-1976-0424630-2

Keywords:
Distributive pseudocomplemented lattice,
sheaf representation,
-ideal,
congruences

Article copyright:
© Copyright 1976
American Mathematical Society