Geodesic
The regular radical of semigroup rings of commutative semigroups
Glasgow mathematical journal, Tome 34 (1992) no. 2, pp. 133-141

Voir la notice de l'article provenant de la source Cambridge University Press

A description of regular group rings is well known (see [12]). Various authors have considered regular semigroup rings (see [17], [8], [10], [11], [4]). These rings have been characterized for many important classes of semigroups, although the general problem turns out to be rather difficult and still has not got a complete solution. It seems natural to describe the regular radical in semigroup rings for semigroups of the classes mentioned. In [10], the regular semigroup rings of commutative semigroups were described. The aim of the present paper is to characterize the regular radical ρ(R[S]) for each associative ring R and commutative semigroup S. 
Kelarev, A. V. The regular radical of semigroup rings of commutative semigroups. Glasgow mathematical journal, Tome 34 (1992) no. 2, pp. 133-141. doi: 10.1017/S001708950000865X
@article{10_1017_S001708950000865X,
     author = {Kelarev, A. V.},
     title = {The regular radical of semigroup rings of commutative semigroups},
     journal = {Glasgow mathematical journal},
     pages = {133--141},
     year = {1992},
     volume = {34},
     number = {2},
     doi = {10.1017/S001708950000865X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950000865X/}
}
TY  - JOUR
AU  - Kelarev, A. V.
TI  - The regular radical of semigroup rings of commutative semigroups
JO  - Glasgow mathematical journal
PY  - 1992
SP  - 133
EP  - 141
VL  - 34
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708950000865X/
DO  - 10.1017/S001708950000865X
ID  - 10_1017_S001708950000865X
ER  - 
%0 Journal Article
%A Kelarev, A. V.
%T The regular radical of semigroup rings of commutative semigroups
%J Glasgow mathematical journal
%D 1992
%P 133-141
%V 34
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708950000865X/
%R 10.1017/S001708950000865X
%F 10_1017_S001708950000865X

[1] 1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. 1, Mathematical Surveys No. 7 (American Mathematical Society, 1961). Google Scholar

[2] 2.Goodearl, K. R., von Neumann regular rings (Pitman, 1979). Google Scholar

[3] 3.Jespers, E. and Wauters, P., A description of the Jacobson radical of semigroup rings of commutative semigroups, Group and semigroup rings, Proceedings of Conference, Johannesburg, 1985, Ed. Karpilovsky, G. (North-Holland, 1966), 43–89. Google Scholar

[4] 4.Kelarev, A. V., On regular semigroup rings, Semigroup Forum 40 (1990), 113–114. Google Scholar | DOI

[5] 5.Kelarev, A. V., A description of the radicals of semigroup algebras of commutative semigroups, to appear. Google Scholar

[6] 6.Kelarev, A. V., On the Jacobson radical of semigroup rings of commutative semigroups, Math. Proc. Cambridge Philos. Soc. 108 (1990), 429–433. Google Scholar | DOI

[7] 7.Krempa, J., Radicals of semigroup rings, Fund. Math. 85 (1974), 57–71. Google Scholar | DOI

[8] 8.Munn, W. D., On the regularity of certain semigroup algebras, Semigroups, Proceedings of the Conference held at Monash University, 1979, Ed. Hall, T. E., Jones, P. R. and Preston, G. B. (Academic Press, 1980), 207–224. Google Scholar

[9] 9.Munn, W. D., On commutative semigroup algebras, Math. Proc. Cambridge Philos. Soc. 93 (1983), 237–246. Google Scholar | DOI

[10] 10.Okniński, J., On regular semigroup rings, Proc. Roy. Soc. Edinburgh Sect. A 99 (1984), 145–151. Google Scholar | DOI

[11] 11.Okninski, J., Semigroup rings as excellent extensions and the regular radical, Simon Stevin 61 (1987), 301–311. Google Scholar

[12] 12.Passman, D. S., The algebraic structure of group rings (Wiley-Interscience, 1977). Google Scholar

[13] 13.Passman, D. S., Group rings, crossed products and Galois theory, CBMS Regional Conference Series in Mathematics, 64 (American Mathematical Society, 1986). Google Scholar

[14] 14.Ponizovskiî, I. S., An example of a semiprimitive semigroup algebra, Semigroup Forum 26 (1983), 225–228. Google Scholar | DOI

[15] 15.Ponizovskiî, I. S., On semigroups rings, Semigroup Forum 28 (1984), 143–154. Google Scholar | DOI

[16] 16.Teply, M. L., Turman, E. G. and Quesada, A., On semisimple semigroup rings, Proc. Amer. Math. Soc. 79 (1980), 157–163. Google Scholar | DOI

[17] 17.Weissglass, J., Regularity of semigroup rings, Proc. Amer. Math. Soc. 25 (1970), 499–503. Google Scholar | DOI

Cité par Sources :