On the coefficient ring in a~semigroup ring
Izvestiya. Mathematics , Tome 10 (1976) no. 5, pp. 899-911.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we study the concept of the invariance of a ring relative to a commutative semigroup. Invariance is proved for certain Prüfer rings and affine algebras relative to semigroups of a special class. Bibliography: 11 titles.
@article{IM2_1976_10_5_a0,
     author = {S. G. Vl\u{a}du\c{t}},
     title = {On the coefficient ring in a~semigroup ring},
     journal = {Izvestiya. Mathematics },
     pages = {899--911},
     publisher = {mathdoc},
     volume = {10},
     number = {5},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1976_10_5_a0/}
}
TY  - JOUR
AU  - S. G. Vlăduţ
TI  - On the coefficient ring in a~semigroup ring
JO  - Izvestiya. Mathematics 
PY  - 1976
SP  - 899
EP  - 911
VL  - 10
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1976_10_5_a0/
LA  - en
ID  - IM2_1976_10_5_a0
ER  - 
%0 Journal Article
%A S. G. Vlăduţ
%T On the coefficient ring in a~semigroup ring
%J Izvestiya. Mathematics 
%D 1976
%P 899-911
%V 10
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1976_10_5_a0/
%G en
%F IM2_1976_10_5_a0
S. G. Vlăduţ. On the coefficient ring in a~semigroup ring. Izvestiya. Mathematics , Tome 10 (1976) no. 5, pp. 899-911. http://geodesic.mathdoc.fr/item/IM2_1976_10_5_a0/

[1] Abhyankar S., Eakin P., Heinzer W., “On the uniqueness of the ring of coefficients in a polynomial ring”, J. Algebra, 23 (1972), 310–342 | DOI | MR | Zbl

[2] Eakin P., Heinzer W., “A cancellation problem for rings”, Conference on Commutative Algebra (Univ. Kansas, Lawrence, Kan., 1972), Lecture Notes in Math., 311, Springer, Berlin, 1973, 61–77 | MR

[3] Hochster M., “Non-uniqueness of the ring of coefficients in a polynomial ring”, Proc. Amer. Math. Soc., 34 (1972), 81–82 | DOI | MR | Zbl

[4] Brewer G. W., Rutter E. A., “Isomorphic polynomial rings”, Archiv der Math., 23:5 (1972), 482–488 | MR

[5] Coleman D. B., Enoch E. E., “The uniqueness of coefficient ring in a polynomial ring”, Proc. Amer. Math. Soc., 27 (1971), 247–252 | DOI | MR | Zbl

[6] Parmenter M., Sehgal S., “Uniqueness of the coefficient ring in some group rings”, Can. Math. Bull., 16:4 (1973), 551–555 | MR | Zbl

[7] Gilmer R. G., Parker P., “Semigroup rings as Prüfer rings”, Duke Math. J., 41:1 (1974), 219–230 | DOI | MR | Zbl

[8] Burbaki N., Kommutativnaya algebra, Mir, M., 1973

[9] Trudy matematicheskogo instituta im. V. A. Steklova AN SSSR, LXXV, Nauka, Moskva, 1965 | MR | Zbl

[10] Asanuma T., “On strongly invariant coefficient rings”, Osaca J. Math., 11:3 (1974), 587–593 | MR | Zbl

[11] Nagata M., “A theorem on valuation rings and its application”, Nagoya Math. J., 29 (1967), 85–91 | MR | Zbl