ダウンロード数 : ?
タイトルヨミ
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
日本語以外のタイトル
Injective Hulls of Certain Right Reductive Semigroups as Right S-Systems
ファイル
言語
英語
著者
庄司 邦孝
内容記述(抄録等)
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.
掲載誌名
島根大学理学部紀要
14
開始ページ
25
終了ページ
34
ISSN
03879925
発行日
1980-12-20
NCID
AN00108106
出版者
島根大学理学部
出版者別表記
The Faculty of Science, Shimane University
資料タイプ
紀要論文
ファイル形式
PDF
著者版/出版社版
出版社版
業績ID
e17831
部局
総合理工学部
他の一覧