ADDITIVE GROUPS OF ASSOCIATIVE RINGS
Abstract
An abelian group is said to be semisimple if it is an additive group of at least one semisimple associative ring. It is proved that the description problem for semisimple groups is reduced to the case of reduced groups. As a consequence, it is shown that a torsion free abelian group is semisimple if the rank of its reduced part is less than or equal to , where the infinite cardinal is the rank of its divisible part.
References
1. Beaumont R.A., Lawver D.A. Strongly semisimple abelian groups // Publ. J. Math. 1974. V. 53, № 2. P. 327-336.
2. Eclof P.C., Mez H.C. Additive groups of existentially closed rings // Abelian Groups and Modules: Proceeding of the Udine conference. Vienna-N.York: Springer-Verlag, 1984. P. 243-252.
3. Kompantseva E.I. Semisimple rings on completely decomposable abelian groups // J. of Math. Sciences. 2009. V. 154. № 3. P. 324-332.
Review
For citations:
Kompantseva E.I. ADDITIVE GROUPS OF ASSOCIATIVE RINGS. Civil Aviation High Technologies. 2015;(222):159-163. (In Russ.)
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