Stone compactification of additive generalized-algebraic lattices

Xueyou Chen; Quingguo Li; Zike Deng

doi:10.4995/agt.2007.1901

Authors

Xueyou Chen Shandong University of Technology
Quingguo Li Hunan University
Zike Deng Hunan University

DOI:

https://doi.org/10.4995/agt.2007.1901

Keywords:

Additivity, Generalized way-below relation, Lower homomorphism, Upper adjoint

Abstract

In this paper, the notions of regular, completely regular, compact additive generalized algebraic lattices are introduced, and Stone compactification is constructed. The following theorem is also obtained.

Theorem: An additive generalized algebraic lattice has a Stone compactification if and only if it is regular and completely regular.

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Author Biographies

Xueyou Chen, Shandong University of Technology

College of Mathematics and Information Science

Quingguo Li, Hunan University

College of Mathematics and Economics

Zike Deng, Hunan University

College of Mathematics and Economics

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