Geodesic
Projective Socles
Canadian mathematical bulletin, Tome 32 (1989) no. 4, pp. 498-499

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DOI

Nicholson and Watters have recently investigated rings with projective socles and they have shown, among other things, that a ring R has a projective socle if and only if each matrix ring Mn(R), n > 1, has a projective socle. We generalize this result by showing that if S is an excellent extension of R, then the socle of R is projective if and only if the socle of S is projective. Examples of excellent extensions include, as well as matrix rings Mn(R), skew group rings R * G where G is a finite group and the order of G is invertible in R.
DOI : 10.4153/CMB-1989-073-1
Mots-clés : 16A50, 16A56 
Stewart, Patrick N. Projective Socles. Canadian mathematical bulletin, Tome 32 (1989) no. 4, pp. 498-499. doi: 10.4153/CMB-1989-073-1
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     author = {Stewart, Patrick N.},
     title = {Projective {Socles}},
     journal = {Canadian mathematical bulletin},
     pages = {498--499},
     year = {1989},
     volume = {32},
     number = {4},
     doi = {10.4153/CMB-1989-073-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-073-1/}
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