On the Jacobson radical of some endomorphism rings (original) (raw)
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Acta Mathematica Academiae Scientiarum Hungaricae
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On p-extensions of commutative rings
Journal of Pure and Applied Algebra, 1991
Ferrero. M.. A. Paques and A. Solecki. On Z,-extensions of commutative rings. Journal af Pure and Applied Algebra 72 (1991) 5-22. We study ZI,,-extensions of a commutative ring R. Some general properties corresponding to the finite Galois theory by Chase, Harrison and Rosenberg are proved. After that. we consider H,-extensions of commutative rings of characteristic p. We describe the structure of a Z,-extension and the H,-module T(Z,. R) of the isomorphism classes of &-extensions of R. via Witt vectors. Results on cyclic p"-extensions of rings of characteristic p, which are already known, are also recovered by direct and elementary methods. * This research was partially supported by CNPq. FAPERGS, FAPESP and FINEP (Brazil). 0022-4049/91/$03.50 0 1991 --Elsevier Science Publishc! B.V. (North-Holland)
Mathematics and Statistics, 2014
In this paper, we have defined the concept of p-map and studied some properties of p-map. By using this map, we have shown that p(G) is a subgroup of G and S = {x : p(x) = e} is a right transversal (with identity) of p(G) in G which becomes group by using p-map and some more conditions. Finally, we have shown that G be an extension of p(G).
3 ADJOINT GROUPS OF p-NIL RINGS AND p-GROUP AUTOMORPHISMS
2016
We introduce a class of rings, namely the class of left or right p-nil rings, for which the adjoint groups behave regularly. Every p-ring is close to being left or right p-nil in the sense that it contains a large ideal belonging to this class. Also their adjoint groups occur naturally as groups of automorphisms of p-groups. These facts and some of their applications are investigated in this paper.