BCC-algebras and residuated partially-ordered groupoid

✍ Scribed by Xiaohong Zhang

• Book ID: 120954950
• Publisher: SP Versita
• Year: 2013
• Tongue: English
• Weight: 275 KB
• Volume: 63
• Category: Article
• ISSN: 0139-9918
• DOI: 10.2478/s12175-013-0104-7

✦ Synopsis

Abstract

The aim of the paper is to investigate the relationship between BCC-algebras and residuated partially-ordered groupoids. We prove that an integral residuated partially-ordered groupoid is an integral residuated pomonoid if and only if it is a double BCC-algebra. Moreover, we introduce the notion of weakly integral residuated pomonoid, and give a characterization by the notion of pseudo-BCI algebra. Finally, we give a method to construct a weakly integral residuated pomonoid (pseudo-BCI algebra) from any bounded pseudo-BCK algebra with pseudo product and any group.