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Paper Information

Title: 

BANASCHEWSKI’S THEOREM FOR S-POSETS: REGULAR INJECTIVITY AND COMPLETENESS

Type: PAPER
Author(s): MAHMOUDI M.,RASOULI H.*
 
 *FACULTY OF MATHEMATICAL SCIENCES, SHAHID BEHESHTI UNIVERSITY 19839, EVIN, TEHRAN, IRAN
 
Name of Seminar: IRANIAN ALGEBRA SEMINAR
Type of Seminar:  CONFERENCE
Sponsor:  TARBIAT MOALLEM UNIVERSITY, FACULTY OF MATHEMATICAL SCIENCES AND COMPUTER
Date:  2009Volume 20
 
 
Abstract: 

IN THIS TALK, THE NOTION OF INJECTIVITY IN THE CATEGORY POS-S OF S-POSETS, FOR A POMONOID S, IS DISCUSSED. FIRST WE SEE THAT, ALTHOUGH THERE IS NO NON-TRIVIAL INJECTIVE S-POSET WITH RESPECT TO MONOMORPHISMS, POS-S HAS ENOUGH (REGULAR) INJECTIVES WITH RESPECT TO REGULAR MONOMORPHISMS (SUB S-POSETS). THEN, RECALLING BANASCHEWSKI’S THEOREM WHICH STATES THAT REGULAR INJECTIVITY OF POSETS WITH RESPECT TO ORDER-EMBEDDINGS AND COMPLETENESS ARE EQUIVALENT, WE STUDY IT FOR S-POSETS AND GET SOME HOMOLOGICAL CLASSIFICATION OF POMONOIDS AND POGROUPS. AMONG OTHER THINGS, WE ALSO SEE THAT REGULAR INJECTIVE S-POSETS ARE EXACTLY THE RETRACTS OF COFREE S-POSETS OVER COMPLETE POSETS.

 
Keyword(s): S-POSET, REGULAR INJECTIVITY, COMPLETENESS
 
 
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