Quotients and subalgebras of sup-algebras

Proceedings of the Estonian Academy of Sciences

Xia Zhang¹  Valdis Laan¹ 

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关键词: sup-algebra;    nucleus;    conucleus;    congruence;    quotient;    subalgebra;   

DOI  :  10.3176/proc.2015.3.16

学科分类：化学（综合）

来源: Teaduste Akadeemia Kirjastus

【 摘 要 】

An ordered algebra is called a sup-algebra if its underlying poset is a complete lattice and its operations are compatible with joins in each variable. In this article we study quotients and subalgebras of sup-algebras. We show that the congruence lattice of a sup-algebra is isomorphic to the lattice of its nuclei and dually isomorphic to the lattice of its meet-closed subalgebras. We also prove that the lattice of subalgebras of a sup-algebra is isomorphic to the lattice of its conuclei.

【 授权许可】

Unknown