ISSN:
1572-8730
Schlagwort(e):
global subdirect product
;
sheaf
;
lattice ordered algebra
;
Nachbin's theorem
;
Chinese remainder theorem
;
Priestley duality
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
,
Philosophie
Notizen:
Abstract Given a variety ν we study the existence of a class ℱ such that S1 every A ε ν can be represented as a global subdirect product with factors in ℱ and S2 every non-trivial A ε ℱ is globally indecomposable. We show that the following varieties (and its subvarieties) have a class ℱ satisfying properties S1 and S2: p-algebras, distributive double p-algebras of a finite range, semisimple varieties of lattice expansions such that the simple members form a universal class (bounded distributive lattices, De Morgan algebras, etc) and arithmetical varieties in which the finitely subdirectly irreducible algebras form a universal class (f-rings, vector groups, Wajsberg algebras, discriminator varieties, Heyting algebras, etc). As an application we obtain results analogous to that of Nachbin saying that if every chain of prime filters of a bounded distributive lattice has at most length 1, then the lattice is Boolean.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF00370143
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