| Paper title: |
Left QI-rings with constraints |
| Published in: | Issue 2, (Vol. 19) / 2025 |
| Pages: | 3-12 |
| Author(s): | Ion BUNU, Olga CHICU |
| Abstract. | In the R-Mod category of left R-modules over the associative ring R with unity we study left QI-rings, obtaining, in the case of concrete restrictions, their complete description. |
| Keywords: | Torsion (pretorsion), Essential Ideal, Strongly Semiprime Rings, PQ-rings, QI-rings. |
| References: | [1]. Faith C. Algebra: rings, modules and categories. V.1. M.: Mir, 1977 (in Russian). [2]. Faith C. Algebra: rings, modules and categories. V.2. M.: Mir, 1979 (in Russian). [3]. Sharpe D.W., Wamos P. Injective modules. Cambridge Univ. Press, 1972. [4]. Bican L., Kepka T., Nemec P. Rings, modules and preradicals. Marcel Dekker, 1982. [5]. Guţan M., Guţan G., Radu Gh., Ştefanescu M., Preradicals and torsion theories.Universitatea „Al. Ioan Cuza” Ia.i, Facultatea de Matematica, 1986. [6]. Kashu A.I. Radicals and torsion in modules. Chisinau, .tiinta, 1983 (in Russian). [7]. Stenström B., Rings of quotiens. Springer Verlag, Berlin, 1975. [8]. Andrunakievic A.V. About quite simple one-sided ideals, no.1, pp 10-15. [9]. Boyle A.K., Goodearl K.R., Rings over wich certain modules are injective. Pacif. J.Math., V.58, no.1, 1975. [10]. Beachy J.A. A generalization of injectivity. Pacif. J.Math., no.2, 1972, pp. 313-327. [11]. Bunu I.D. On left-QI-rings. Mat. Issld., vyp 49, 1979, pp. 23-34 (in Russian). [12]. Bunu I.D. On rings over which all pretorsion is ideal. Chisinau: Ştiinta, 1983, pp.12-15. [13]. Bunu I.D. On the strongly semiprime rings. Bul. Acad. Ştiinţe Repub., Mold., Mat., no. 1(23), 1997, pp. 78-83. [14]. Bunu I.D. On rings over which the lattice of all pretorsions has only one maximal element. Fundamentalnaya I prikladnaya matematika. V.4, no.1, 1998, pp. 223-231. (in Russian) [15]. Byrd K.A. Rings whose quasi-injective modules are injective. Proc. Amer. Math. Soc., V.33. no. 2, 1972, pp. 235-240. [16]. Faith C. On hereditary rings and Boyle’s conjecture. Arch. Math., V. 27, no. 2, 1976, pp. 113-119. [17]. Handelman D. Strongly semiprime rings. Pacific I. Math., V.60, no.1, 1975, pp.115-122. [18]. Harada M. Note on quasi-injective modules. Osaka I. Math., V.2, 1965, pp. 351-356. [19]. Kashu A.I. Radicals and cogenerators in modules. Mat. Issled., V.XI, no. 2(32), 1974, pp. 53-68 (in Russian) [20]. Koifman L.A. Rings over which singular modules are injective. I. Mat. Issled., v.VI, no. 2(20), 1971, pp. 85-104. (in Russian) |
| Back to the journal content | |
