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Title Transcription
アル ミギ カンヤクテキ ハングン ノ ミギ S システム トシテンノ イニュウテキ ホウラク ニツイテ
Title Alternative
Injective Hulls of Certain Right Reductive Semigroups as Right S-Systems
File
language
eng
Author
Shoji, Kunitaka
Description
Let S be a right reductive semigroup. Then the semigroup S is embedded in the semigroup Λ(S) of all left translations of S as its left ideal. Thus we regard S as a left ideal of Λ(S). Then Λ(S) is an essential extension of S as a right S-system. By Berthiaume [2] there exists the injective hull I(S) of S containing Λ(S) as a right S-subsystem. In §1, we give necessary and sufficient conditions that Λ(S) equals I(S). It turns out that both left zero semigroups and right reductive primitive regular semigroups satisfy any one of these conditions. Consequenly we show that full transformation semigroups (written on the left) and the direct product of columnmonomial matrix semigroups over groups are right self-injective. We also study right nonsingular semigroups, semilattices of groups S which satisfy the condition that Λ(S) = I(S). In §2, we state some results on right self-injective semigroups. In particular it is shown that any direct product of right self-injective semigroups with O amd 1 is right self-injective. Consequently we show that any direct product of self-injective semigroups is self-injective.
Journal Title
Memoirs of the Faculty of Science, Shimane University
Volume
14
Start Page
25
End Page
34
ISSN
03879925
Published Date
1980-12-20
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
e17831
OAI-PMH Set
Faculty of Science and Engineering