Title Transcription  ミギ ジコ イニュウテキ ハングン ノ ゼッタイ ヘイセイ ニツイテ

Title Alternative  Right SelfInjective Semigroups are Absolutely Closed

File  
language 
eng

Author 
Shoji, Kunitaka

Description  Hinkle [3] has showm that the direct product of column monomial matrix semigroups over groups is right selfinjective. The author [12] has shown that the full transformation semigroup on a nonempty set (written on the left) is right selfinjective and so every semigroup is embedded in a right selfinjective regular semigroup. While absolutely closed semigroups has been first studied in Isbell [7]. In Howie and Isbell [51 and Scheiblich and Moore [8] it has been shown that inverse semigroups, totally divisionordered semigroups, right [left] simple semigroups, finite cyclic semigroups and full transformation semigroups are absolutely closed. In §1 we show that every right [left] selfinjective semigrowp is absolutely closed. This gives alternative proofs that right [left] simple semigroups, finite cyclic semigroups and full transformation semigroups are absolutely closed. By using a result of [5] we show that the class of right [left] selfiujective [regular] semigrowps has the special amalgamation property. In §2 we show that a commutative separative semigroup is absolutely closed if and only if it is a semilattice of abelian groups. By using a characterization of selfinjective inverse semigroups [9] we give a structure theorem for selfinjective commutative separative semigroups.

Journal Title 
Memoirs of the Faculty of Science, Shimane University

Volume  14

Start Page  35

End Page  39

ISSN  03879925

Published Date  19801220

NCID  AN00108106

Publisher  島根大学理学部

Publisher Aalternative  The Faculty of Science, Shimane University

NII Type 
Departmental Bulletin Paper

Format 
PDF

Text Version 
出版社版

Gyoseki ID  e17829

OAIPMH Set 
Faculty of Science and Engineering
