Baer Endomorphism Rings and Closure Operators

Khuri, Soumaya M.

Canadian journal of mathematics, Tome 30 (1978) no. 5, pp. 1070-1078

Résumé

A Baer ring is a ring in which every right (and left) annihilator ideal is generated by an idempotent. Generalizing quite naturally from the fact that the endomorphism ring of a vector space is a Baer ring, Wolfson [5; 6] investigated questions such as when the endomorphism ring of a free module is a Baer ring, and when the ring of continuous linear transformations on a pair of dual vector spaces is a Baer ring. A further generalization was made in [7], where the question of when the endomorphism ring of a torsion-free module over a semiprime left Goldie ring is a Baer ring was treated.

Détail

DOI : 10.4153/CJM-1978-089-x

Bibliographie

[1] 1. Faith, C., Lectures on infective modules and quotient rings, Springer-Verlag lecture notes J+9 (1967). Google Scholar

[2] 2. Goodearl, K. R., Ring theory (Marcel Dekker, 1976). Google Scholar

[3] 3. Stenstrom, B., Rings of quotients, Springer-Verlag, Grundlehren der mathematischen Wissenschaften 7 (1975). Google Scholar

[4] 4. Utumi, Y., On rings of which any one-sided quotient ring is two-sided, Proc. Amer. Math. Soc. 14 (1963), 141–147. Google Scholar

[5] 5. Wolfson, K. G., A class of primitive rings, Duke Math. J. 22 (1955), 157–163. Google Scholar

[6] 6. Wolfson, K. G., Baer rings of endomorphisms, Math. Annalen 1-3 (1961), 19–28. Google Scholar

[7] 7. Khuri, S. M., Baer rings of endomorphisms, Ph.D. dissertation, Yale University, 1974. Google Scholar

[8] 8. Zelmanowitz, J. M., Endomorphism rings of torsionless modules, J. Alg. 5 (1967), 325–341. Google Scholar