In this paper we study the notions of cogenerator and subdirectly irreducible in the category of S-poset. First we give some necessary and sufficient conditions for a cogenerator $S$-posets. Then we see that under some conditions, regular injectivity implies generator and cogenerator. Recalling Birkhoff's Representation Theorem for algebra, we study subdirectly irreducible S-posets and give this theorem for the category of ordered right acts over an ordered monoid. Among other things, we give the relations between cogenerators and subdirectly irreducible S-posets.
Moghaddasi, G. (2015). COGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF S-POSETS. Journal of Algebraic Systems, 2(2), 137-146. doi: 10.22044/jas.2015.371
MLA
Gh. Moghaddasi. "COGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF S-POSETS", Journal of Algebraic Systems, 2, 2, 2015, 137-146. doi: 10.22044/jas.2015.371
HARVARD
Moghaddasi, G. (2015). 'COGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF S-POSETS', Journal of Algebraic Systems, 2(2), pp. 137-146. doi: 10.22044/jas.2015.371
VANCOUVER
Moghaddasi, G. COGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF S-POSETS. Journal of Algebraic Systems, 2015; 2(2): 137-146. doi: 10.22044/jas.2015.371
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