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On Right FGP-Injective Rings
| Content Provider | CiteSeerX |
|---|---|
| Author | Aly, Farahat Sayed |
| Abstract | Abstract. This paper invistigates right FGP-injective rings with ACC on annihilators It is shown that if R is a right Kasch, right FGP-injective, then the left socle equals the right socle that is essential on the left, and the two singular ideals coincide, if R is semiperfect right FGP-injective and has essential right socle, then R is left and right Kasch ring. If R is semiprime right FGP-injective, then every maximal right (left) annihilator of R is maximal right (left) ideal of R generated by an idempotent, if R is right FGP-injective ring and the ascending chain r(a1) ⊆ r(a2a1) ⊆ r(a3a2a1) ⊆ · · · terminates for every infinite sequence a1, a1, a3, · · · of R, then R is right perfect. An affirmative answer to a conjecture of Azumaya [5] is given for right FGP-injective ring. |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Right Fgp-injective Ring Maximal Right Right Socle Essential Right Socle Singular Ideal Infinite Sequence A1 Right Perfect Right Kasch Ascending Chain Affirmative Answer Semiprime Right Fgp-injective Right Kasch Ring Semiperfect Right Fgp-injective Left Socle |
| Content Type | Text |
| Resource Type | Article |