Yıl 2015, Cilt 17, Sayı 17, Sayfalar 199 - 214 2015-06-01
| | | |

## ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS

#### Victor Camillo [1] , W. Keith Nicholson [2]

##### 188 245

The rings in the title are studied and related to right principally injective rings. Many properties of these rings (called left pseudo-morphic by Yang) are derived, and conditions are given that an endomorphism ring is left pseudo-morphic. Some particular results: (1) Commutative pseudo-morphic rings are morphic; (2) Semiprime left pseudo-morphic rings are semisimple; and (3) A left and right pseudo-morphic ring satisfying (equivalent) mild finiteness conditions is a morphic, quasi-Frobenius ring in which every onesided ideal is principal. Call a left ideal L a left principal annihilator if L = l(a) = {r ∈ R | ra = 0} for some a ∈ R. It is shown that if R is left pseudo-morphic, left mininjective ring with the ACC on left principal annihilators then R is a quasi-Frobenius ring in which every right ideal is principal and every left ideal is a left principal annihilator.
Regular rings, morphic rings, quasi-morphic rings, pseudo-morphic rings, artinian principal ideal rings, quasi-Frobenius rings
Konular JA77FH99TM Makaleler Yazar: Victor Camillo Yazar: W. Keith Nicholson
 Bibtex @ { ieja266221, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2015}, volume = {17}, pages = {199 - 214}, doi = {10.24330/ieja.266221}, title = {ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS}, key = {cite}, author = {Nicholson, W. Keith and Camillo, Victor} } APA Camillo, V , Nicholson, W . (2015). ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS. International Electronic Journal of Algebra, 17 (17), 199-214. DOI: 10.24330/ieja.266221 MLA Camillo, V , Nicholson, W . "ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS". International Electronic Journal of Algebra 17 (2015): 199-214 Chicago Camillo, V , Nicholson, W . "ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS". International Electronic Journal of Algebra 17 (2015): 199-214 RIS TY - JOUR T1 - ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS AU - Victor Camillo , W. Keith Nicholson Y1 - 2015 PY - 2015 N1 - doi: 10.24330/ieja.266221 DO - 10.24330/ieja.266221 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 199 EP - 214 VL - 17 IS - 17 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266221 UR - http://dx.doi.org/10.24330/ieja.266221 Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS %A Victor Camillo , W. Keith Nicholson %T ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS %D 2015 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 17 %N 17 %R doi: 10.24330/ieja.266221 %U 10.24330/ieja.266221 ISNAD Camillo, Victor , Nicholson, W. Keith . "ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS". International Electronic Journal of Algebra 17 / 17 (Haziran 2015): 199-214. http://dx.doi.org/10.24330/ieja.266221