Pseudo-injective modules which are not quasi-injective

Teply, Mark L.

doi:10.1090/S0002-9939-1975-0366977-3

Pseudo-injective modules which are not quasi-injective
HTML articles powered by AMS MathViewer

by Mark L. Teply

Proc. Amer. Math. Soc. 49 (1975), 305-310

DOI: https://doi.org/10.1090/S0002-9939-1975-0366977-3

PDF | Request permission

Abstract:

For certain rings with infinitely many nonisomorphic simple left modules, a method is given for constructing pseudo-injective modules which are not quasi-injective. This method is used to produce examples of such modules over a commutative ring.

References

L. Fuchs, Torsion preradicals and ascending Loewy series of modules, J. Reine Angew. Math. 239(240) (1969), 169–179. MR 285565, DOI 10.1515/crll.1969.239-240.169

Injective modules and their generalizations

S. K. Jain and Surjeet Singh, Quasi-injective and pseudo-injective modules, Canad. Math. Bull. 18 (1975), no. 3, 359–366. MR 396669, DOI 10.4153/CMB-1975-065-3
R. E. Johnson and E. T. Wong, Quasi-injective modules and irreducible rings, J. London Math. Soc. 36 (1961), 260–268. MR 131445, DOI 10.1112/jlms/s1-36.1.260
Surjeet Singh and S. K. Jain, On pseudo injective modules and self pseudo injective rings, J. Math. Sci. 2 (1967), 23–31. MR 0219569
Surjeet Singh and Kamlesh Wasan, Pseudo-injective modules over commutative rings, J. Indian Math. Soc. (N.S.) 34 (1970), 61–65 (1971). MR 289486