On $p$-injectivity, YJ-injectivity and quasi-Frobeniusean rings
Yue Chi Ming, Roger
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002), p. 33-42 / Harvested from Czech Digital Mathematics Library
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A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characterized in terms of special annihilators. Quasi-Frobeniusean rings are characterized in terms of $p$-injectivity. Also, a commutative YJ-injective ring with maximum condition on annihilators and finitely generated socle is quasi-Frobeniusean.

Publié le : 2002-01-01
Classification:  16D30,  16D36,  16D50,  16E50,  16L60,  16N60,  16P20 
@article{119298,
     author = {Roger Yue Chi Ming},
     title = {On $p$-injectivity, YJ-injectivity and quasi-Frobeniusean rings},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {43},
     year = {2002},
     pages = {33-42},
     zbl = {1068.16004},
     mrnumber = {1903305},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119298}
}

Yue Chi Ming, Roger. On $p$-injectivity, YJ-injectivity and quasi-Frobeniusean rings. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 33-42. http://gdmltest.u-ga.fr/item/119298/

Baccella G. Generalized $V$-rings and von Neumann regular rings, Rend. Sem. Mat. Univ. Padova 72 (1984), 117-133. (1984) | MR 0778337 | Zbl 0547.16006

Chase S.U. Direct product of modules, Trans. Amer. Math. Soc. 97 (1960), 457-473. (1960) | MR 0120260

Faith C. Algebra II: Ring Theory, Grundlehren Math. Wiss. 191 (1976). (1976) | MR 0427349

Faith C. Rings and things and a fine array of twentieth century associative algebra, AMS Math. Survey and Monographs 65 (1999). (1999) | MR 1657671

Goodearl K.R. Von Neumann Regular Rings, Pitman, 1979. | MR 0533669 | Zbl 0841.16008

Hirano Y.; Tominaga H. Regular rings, $V$-rings and their generalizations, Hiroshima Math. J. 9 (1979), 137-149. (1979) | MR 0529329 | Zbl 0413.16015

Hirano Y. On non-singular $p$-injective rings, Publ. Math. 38 (1994), 455-461. (1994) | MR 1316640

Huynh D.V.; Dung N.V. A characterization of Artinian rings, Glasgow Math. J. 30 (1988), 67-73. (1988) | MR 0925560 | Zbl 0637.16012

Huynh D.V.; Dung N.V. Rings with restricted injective condition, Arch. Math. 54 (1990), 539-548. (1990) | MR 1052974 | Zbl 0703.16003

Huynh D.V.; Dung N.V.; Smith P.F.; Wisbauer R. Extending Modules, Pitman, London, 1994. | Zbl 0841.16001

Mohamed S.H.; Mueller B.J. Continous and discrete modules, LMS Lecture Note 47 (C.U.P.), 1990.

Puninski G.; Wisbauer R.; Yousif M.F. On $p$-injective rings, Glasgow Math. J. 37 (1995), 373-378. (1995) | MR 1355393 | Zbl 0847.16005

Wang Ding Guo Rings chracterized by injectivity classes, Comm. Algebra 24 (1996), 717-726. (1996) | MR 1373501

Wisbauer R. Foundations of Module and Ring Theory, Gordon and Breach, New-York, 1991. | MR 1144522 | Zbl 0746.16001

Xue Wei Min A note on ${YJ}$-injectivity, Riv. Mat. Univ. Parma (6) 1 (1998), 31-37. (1998) | MR 1680954

Xue Wei Min Rings related to quasi-Frobenius rings, Algebra Colloq. 5 (1998), 471-480. (1998) | MR 1683093

Yue Chi Ming R. On von Neumann regular rings, Proc. Edinburgh Math. Soc. 19 (1974), 89-91. (1974) | MR 0342553

Yue Chi Ming R. On simple $p$-injective modules, Math. Japonica 19 (1974), 173-176. (1974) | MR 0399167 | Zbl 0263.16019

Yue Chi Ming R. On regular rings and continuous rings, Math. Japonica 24 (1979), 563-571. (1979) | MR 0565541

Yue Chi Ming R. On $V$-rings and prime rings, J. Algebra 62 (1980), 13-20. (1980) | MR 0561114 | Zbl 0429.16018

Yue Chi Ming R. On regular rings and Artinian rings, Riv. Mat. Univ. Parma (4) 8 (1982), 443-452. (1982) | MR 0706868 | Zbl 0516.16006

Yue Chi Ming R. On von Neumann regular rings, X, Collectanea Math. 34 (1983), 81-94. (1983) | MR 0747858 | Zbl 0544.16006

Yue Chi Ming R. On regular rings and continuous rings, III, Annali di Matematica 138 (1984), 245-253. (1984) | MR 0779545 | Zbl 0558.16004

Yue Chi Ming R. On regular rings and Artinian rings, II, Riv. Mat. Univ. Parma (4) 11 (1985), 101-109. (1985) | MR 0851520 | Zbl 0611.16011

Yue Chi Ming R. On von Neumann regular rings, XV, Acta Math. Vietnamica 13 2 (1988), 71-79. (1988) | MR 1023706 | Zbl 0685.16009

Yue Chi Ming R. On $V$-rings, $p$-$V$-rings and injectivity, Kyungpook Math. J. 32 (1992), 219-228. (1992) | MR 1203937 | Zbl 0786.16008

Yue Chi Ming R. On self-injectivity and regularity, Rend. Sem. Fac. Sci. Univ. Cagliari 64 (1994), 9-24. (1994) | MR 1356180 | Zbl 0870.16003

Zhang Jule Fully idempotent rings whose every maximal left ideal is an ideal, Chinese Sci. Bull. 37 (1992), 1065-1068. (1992) | MR 1321903

Zhang Jule A note on von Neumann regular rings, Southeast Asian Bull. Math. 22 (1998), 231-235. (1998) | MR 1684237 | Zbl 0923.16011

Zhang Jule; Wu Jun Generalizations of principal injectivity, Algebra Colloq. 6 (1999), 277-282. (1999) | MR 1809647 | Zbl 0949.16002