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There have been some study characterizing monoids by homological classi cation using the properties around projectivity,injectivity, or regularity of acts. In particular Kilp and Knauer([4])have analyzed monoids over which all acts with one of the prop-erties around projectivity or injectivity are regular. However Kilp and Knauer left over problems of characterization of monoids over which all regular right S-acts are (weakly) at, (weakly) injective or faithful. Among these open problems, Liu([3]) proved that all regular right S-acts are (weakly) at if and only if es is a von Neu-mann regular element of S for all s 2 S and e2 = e 2 T, and that all regular right S-acts are faithful if and only if all right ideals eS,e2 = e 2 T, are faithful. But it still remains an open question to characterize over which all regular right S-acts are weakly injective or injective. Hence the purpose of this study is to investigate the relations between regular right S-acts and weakly injective right S-acts, and then characterize the monoid over which all regular right S-acts are weakly injective.
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참고문헌 (7)
참고문헌 신청
J. Zelmanowitz / 1972 / Regular modules / Trans. Amer. Math. Soc 163 : 341 ~ 355
Liu Zhongkui / 1993 / A characterization of regular monoids by atness of left acts / Semi- group Forum 46 : 85 ~ 89
Liu Zhongkui / 1995 / Monoids over which all regular left acts are at / Semigroup Forum 50 : 135 ~ 139
Liu Zhongkui / 1996 / Monoids over which all at left acts are regular / J. Pure Appl. Algebra 111 : 199 ~ 203
Mati Kilp / 1987 / Characterization of monoids by properties of regular acts / J. Pure Appl. Algebra 46 : 217 ~ 231
Liu Zhongkui / 1993 / A characterization of regular monoids by atness of left acts / Semi- group Forum 46 : 85 ~ 89
Liu Zhongkui / 1995 / Monoids over which all regular left acts are at / Semigroup Forum 50 : 135 ~ 139
Liu Zhongkui / 1996 / Monoids over which all at left acts are regular / J. Pure Appl. Algebra 111 : 199 ~ 203
Mati Kilp / 1987 / Characterization of monoids by properties of regular acts / J. Pure Appl. Algebra 46 : 217 ~ 231
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