VNR rings, Π -regular rings and annihilators

Roger Yue Chi Ming

Commentationes Mathematicae Universitatis Carolinae (2009)

  • Volume: 50, Issue: 1, page 25-36
  • ISSN: 0010-2628

Abstract

top
Von Neumann regular rings, hereditary rings, semi-simple Artinian rings, self-injective regular rings are characterized. Rings which are either strongly regular or semi-simple Artinian are considered. Annihilator ideals and Π -regular rings are studied. Properties of WGP-injectivity are developed.

How to cite

top

Yue Chi Ming, Roger. "VNR rings, $\Pi $-regular rings and annihilators." Commentationes Mathematicae Universitatis Carolinae 50.1 (2009): 25-36. <http://eudml.org/doc/32478>.

@article{YueChiMing2009,
abstract = {Von Neumann regular rings, hereditary rings, semi-simple Artinian rings, self-injective regular rings are characterized. Rings which are either strongly regular or semi-simple Artinian are considered. Annihilator ideals and $\Pi $-regular rings are studied. Properties of WGP-injectivity are developed.},
author = {Yue Chi Ming, Roger},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {von Neumann regular; $\Pi $-regular; annihilators; $p$-injective; YJ-injective; WGP-injective; semi-simple Artinian; von Neumann regular rings; -regular rings; annihilators; p-injective rings; YJ-injective rings; WGP-injective rings; semi-simple Artinian rings},
language = {eng},
number = {1},
pages = {25-36},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {VNR rings, $\Pi $-regular rings and annihilators},
url = {http://eudml.org/doc/32478},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Yue Chi Ming, Roger
TI - VNR rings, $\Pi $-regular rings and annihilators
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 1
SP - 25
EP - 36
AB - Von Neumann regular rings, hereditary rings, semi-simple Artinian rings, self-injective regular rings are characterized. Rings which are either strongly regular or semi-simple Artinian are considered. Annihilator ideals and $\Pi $-regular rings are studied. Properties of WGP-injectivity are developed.
LA - eng
KW - von Neumann regular; $\Pi $-regular; annihilators; $p$-injective; YJ-injective; WGP-injective; semi-simple Artinian; von Neumann regular rings; -regular rings; annihilators; p-injective rings; YJ-injective rings; WGP-injective rings; semi-simple Artinian rings
UR - http://eudml.org/doc/32478
ER -

References

top
  1. Armendariz E.P., Fisher J.W., Steinberg S.A., 10.1090/S0002-9939-1974-0352164-0, Proc. Amer. Math. Soc. 46 (1974), 315--321. (1974) Zbl0267.16003MR0352164DOI10.1090/S0002-9939-1974-0352164-0
  2. Baccella G., Generalized V -rings and von Neumann regular rings, Rend. Sem. Mat. Univ. Padova 72 (1984), 117--133. (1984) Zbl0547.16006MR0778337
  3. Bass H., 10.1090/S0002-9947-1960-0157984-8, Trans. Amer. Math. Soc. 95 (1960), 466--488. (1960) MR0157984DOI10.1090/S0002-9947-1960-0157984-8
  4. Chase S.U., 10.1090/S0002-9947-1960-0120260-3, Trans. Amer. Math. Soc. 97 (1960), 457--473. (1960) MR0120260DOI10.1090/S0002-9947-1960-0120260-3
  5. Ding N.Q., Chen J.L., Rings whose simple singular models are YJ-injective, Math. Japon. 40 (1994), 191--195. (1994) MR1288035
  6. Faith C., 10.1007/978-3-642-65321-6, Grundlehren Math. Wiss. 191 (1976). (1976) MR0427349DOI10.1007/978-3-642-65321-6
  7. Faith C., Rings and things and a fine array of twentieth century associative algebra, AMS Math. Survey and Monographs 65 (1999). (1999) MR1657671
  8. Goodearl K.R., Ring Theory. Nonsingular Rings and Modules, Pure and Applied Mathematics, no. 33, Marcel Dekker, New York, 1976. Zbl0336.16001MR0429962
  9. Goodearl K.R., Von Neumann Regular Rings, Pitman, Boston, 1979. Zbl0841.16008MR0533669
  10. Hirano Y., On non-singular p -injective rings, Publ. Math. 38 (1994), 455--461. (1994) 
  11. Jain S.K., Mohamed S.H., Singh S., 10.2140/pjm.1969.31.73, Pacific J. Math. 31 (1969), 73--79. (1969) MR0251073DOI10.2140/pjm.1969.31.73
  12. Jans J.P., 10.2140/pjm.1959.9.1103, Pacific J. Math. 9 (1959), 1103--1108. (1959) Zbl0231.16012MR0112904DOI10.2140/pjm.1959.9.1103
  13. Kasch F., Modules and Rings, London Mathematical Society Monographs, 17, Academic Press, London-New York, 1982. Zbl0832.16002MR0667346
  14. Kim N.K., Nam S.B., Kim J.Y., 10.1080/00927879908826551, Comm. Algebra 27 (1999), 2087--2096. (1999) Zbl0923.16008MR1683853DOI10.1080/00927879908826551
  15. Michler, G.O., Villamayor O.E., 10.1016/0021-8693(73)90088-4, J. Algebra 25 (1973), 185--201. (1973) Zbl0258.16023MR0316505DOI10.1016/0021-8693(73)90088-4
  16. Nam S.B., Kim N.K., Kim J.Y., 10.1080/00927879508825543, Comm. Algebra 23 (1995), 5437--5444. (1995) Zbl0840.16006MR1363614DOI10.1080/00927879508825543
  17. Posner E.C., 10.1090/S0002-9939-1960-0111765-5, Proc. Amer. Math. Soc. 11 (1960), 180--184. (1960) Zbl0215.38101MR0111765DOI10.1090/S0002-9939-1960-0111765-5
  18. Puninski G., Wisbauer R., Yousif M.F., 10.1017/S0017089500031657, Glasgow Math. J. 37 (1995), 373--378. (1995) Zbl0847.16005MR1355393DOI10.1017/S0017089500031657
  19. Storrer H.H., 10.4153/CMB-1969-036-9, Canad. Math. Bull. 12 (1969), 287--292. (1969) MR0251075DOI10.4153/CMB-1969-036-9
  20. Tuganbaev A., Rings Close to Regular, Mathematics and its Applications, 545, Kluwer Academic Publishers, Dordrecht, 2002. Zbl1120.16012MR1958361
  21. Tuganbaev A., 10.1016/S1570-7954(03)80071-2, Handbook of Algebra, vol. 3, North-Holland, Amsterdam, 2003. Zbl1080.16008MR2035106DOI10.1016/S1570-7954(03)80071-2
  22. Wisbauer R., Foundations of Module and Ring Theory, Gordon and Breach, New York, 1991. Zbl0746.16001MR1144522
  23. Xue Wei Min, A note on Y J -injectivity, Riv. Mat. Univ. Parma (6) 1 (1998), 31--37. (1998) MR1680954
  24. Yousif M.F., On SI-modules, Math. J. Okayama Univ. 28 (1986), 133--146. (1986) MR0885022
  25. Yue Chi Ming R., 10.2748/tmj/1178242946, Tôhoku Math. J. 21 (1969), 337--342. (1969) Zbl0164.34702MR0252444DOI10.2748/tmj/1178242946
  26. Yue Chi Ming R., On von Neumann regular rings, Proc. Edinburgh Math. Soc. 19 (1974), 89--91. (1974) MR0342553
  27. Yue Chi Ming R., On von Neumann regular rings II, Math. Scan. 39 (1976), 167--170. (1976) MR0435131
  28. Yue Chi Ming R., On annihilator ideals, Math. J. Okayama Univ. 19 (1976), 51--53. (1976) Zbl0348.16008MR0435130
  29. Yue Chi Ming R., 10.1007/BF01659723, Monatsh. Math. 86 (1978), 251--257. (1978) Zbl0414.16006MR0517029DOI10.1007/BF01659723
  30. Yue Chi Ming R., On generalizations of V -rings and regular rings, Math. J. Okayama Univ. 20 (1978), 123--129. (1978) Zbl0402.16014MR0519559
  31. Yue Chi Ming R., On injective and p-injective modules, Riv. Mat. Univ. Parma (4) 7 (1981), 187--197. (1981) Zbl0499.16015MR0671367
  32. Yue Chi Ming R., On regular and continuous rings II, Kyungpook Math. J. 21 (1981), 171--178. (1981) Zbl0516.16007MR0644587
  33. Yue Chi Ming R., On quasi-Frobenius rings and Artinian rings, Publ. Inst. Math. (Beograd) 33 (47) (1983), 239--245. (1983) MR0723453
  34. Yue Chi Ming R., On regular rings and self-injective rings II, Glasnik Mat. 18 (38) (1983), 221--229. (1983) Zbl0528.16006MR0733161
  35. Yue Chi Ming R., On regular rings and Artinian rings II, Riv. Mat. Univ. Parma (4) 11 (1985), 101--109. (1985) Zbl0611.16011MR0851520
  36. Yue Chi Ming R., On von Neumann regular rings XI, Bull. Math. Soc. Sci. Math. Roumanie 30 (76) (1986), 371--379. (1986) Zbl0608.16018MR0892874
  37. Yue Chi Ming R., On injectivity and p-injectivity, J. Math. Kyoto Univ. 27 (1987), 439--452. (1987) Zbl0655.16012MR0910229
  38. Yue Chi Ming R., A note on injective rings, Hokkaido Math. J. 21 (1992), 231--238. (1992) Zbl0777.16001MR1169790
  39. Yue Chi Ming R., On p-injectivity and generalizations, Riv. Mat. Univ. Parma (5) 5 (1996), 183--188. (1996) Zbl0877.16002MR1456411
  40. Yue Chi Ming R., On YJ-injectivity and VNR rings, Bull. Math, Soc. Sci. Math. Roumanie 46 (94) (2003), 87--97. (2003) Zbl1084.16501MR2097354
  41. Zelmanowitz J., 10.4153/CJM-1971-115-x, Canad. J. Math. 27 (1971), 1094--1101. (1971) MR0289567DOI10.4153/CJM-1971-115-x
  42. Zhang J.L., Fully idempotent rings whose every maximal left ideal is an ideal, Chinese Sci. Bull. 37 (1992), 1065--1068. (1992) MR1321903
  43. Zhang J.L., Wu J., Generalizations of principal injectivity, Algebra Colloq. 6 (1999), 277--282. (1999) Zbl0949.16002MR1809647

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.