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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: SEMINAR ON ALGEBRA (SALG20)
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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