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Journal of Algebraic Systems
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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
Gholamreza 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
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
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

COGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF S-POSETS

Article 5, Volume 2, Issue 2, Winter and Spring 2015, Page 137-146  XML PDF (271 K)
Document Type: Original Manuscript
DOI: 10.22044/jas.2015.371
Author
Gholamreza Moghaddasi
Hakim Sabzevary university, Sabzevar, Iran
Abstract
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.
Keywords
S-poset; cogenerator; regular injective; subdirectly irreducible
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