Representation of universal algebras by sheaves

Representation of Universal Algebras by Sheaves

It is proved that every (universal) algebra A with distributive and permutable structure lattice is isomorphic with the algebra of all global sections with compact supports of a sheaf of homomorphic images of A over a topological space. This completely generalises the corresponding result of Klaus Keimel for /-rings. Introduction. The following note is a preliminary report on the investigations...

Representation of Pre A∗-Algebras by Sections of Sheaves

In this paper, we prove that every Pre A∗-algebra A with 1 is isomorphic to the Pre A∗-algebra of all global sections of a sheaf of indecomposable Pre A∗-algebra over Boolean space and that sheaf of indecomposable Pre A∗-algebra with 1 over Boolean space is isomorphic to the sheaf obtained from the Pre A∗-algebra of all sections of the sheaf. Copyright c © 2011 Yang’s Scientific Research Instit...

Sheaves of Algebras

2 Sheaves of Algebras 2 2.1 Direct and inverse image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Generating Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Special Sheaves of Algebras

Fuzzy universal algebras on $L$-sets

This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphi...