BCC-algebras and residuated partially-ordered groupoid |
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| Authors: | Xiaohong Zhang |
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| Affiliation: | 1104. Department of Mathematics, College of Arts and Sciences, Shanghai Maritime University, Shanghai, 201306, P.R.China
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| 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. |
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