Geodesic
Primitive $m$-near-rings over multioperator groups
Sbornik. Mathematics, Tome 13 (1971) no. 2, pp. 247-265 
S. V. Polin. Primitive $m$-near-rings over multioperator groups. Sbornik. Mathematics, Tome 13 (1971) no. 2, pp. 247-265. http://geodesic.mathdoc.fr/item/SM_1971_13_2_a3/
@article{SM_1971_13_2_a3,
     author = {S. V. Polin},
     title = {Primitive $m$-near-rings over multioperator groups},
     journal = {Sbornik. Mathematics},
     pages = {247--265},
     year = {1971},
     volume = {13},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_13_2_a3/}
}
TY  - JOUR
AU  - S. V. Polin
TI  - Primitive $m$-near-rings over multioperator groups
JO  - Sbornik. Mathematics
PY  - 1971
SP  - 247
EP  - 265
VL  - 13
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1971_13_2_a3/
LA  - en
ID  - SM_1971_13_2_a3
ER  - 
%0 Journal Article
%A S. V. Polin
%T Primitive $m$-near-rings over multioperator groups
%J Sbornik. Mathematics
%D 1971
%P 247-265
%V 13
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1971_13_2_a3/
%G en
%F SM_1971_13_2_a3

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

In this article we examine $m\Omega$-near-rings, i.e. $(m+1)$-ary associative ringoids over $\Omega$-groups with one supplementary condition. The concept of a module over an $m\Omega$-near-ring is introduced and, with its aid, the concept of a primitive $m\Omega$-near-ring is introduced, generalizing the idea of a primitive ring. Density theorems are proved for such $m\Omega$-near-rings. With the aid of these theorems, primitive $m\Omega$-near-rings with minimum condition for right ideals are described, and a series of theorems are proved concerning the structure of $m\Omega$-near-rings, which are analogous to simple rings with minimal one-sided ideals. Bibliography: 9 titles.

[1] N. Dzhekobson, Stroenie kolets, IL, Moskva, 1961

[2] N. Jacobson, “Structure theory of simple rings without finiteness assumption”, Trans. Amer. Math. Soc., 57:2 (1945), 228–245 | DOI | MR | Zbl

[3] P. Kon, Universalnaya algebra, Mir, Moskva, 1968 | MR

[4] R. R. Laxton, “Primitive distributively generated near-rings”, Mathematika, 8:1 (1961), 142–158 | MR | Zbl

[5] Lyu Shao-Syue, “O pryamykh slagaemykh v gruppakh s multioperatorami”, Sci. Sinica, 13:11 (1964), 1735–1745 | MR | Zbl

[6] B. I. Plotkin, Gruppy avtomorfizmov algebraicheskikh sistem, Nauka, Moskva, 1966 | MR | Zbl

[7] B. I. Plotkin, “$\Omega$-polugruppy, $\Omega$-koltsa i obschie predstavleniya”, DAN SSSR, 149:5 (1963), 1037–1040 | MR | Zbl

[8] Ya. V. Khion, “$m$-arnye $\Omega$-koltsoidy”, Sib. matem. zh., 8:1 (1967), 174–194 | Zbl

[9] Ya. V. Khion, “$\Omega$-koltsoidy, $\Omega$-koltsa i ikh predstavleniya”, Trudy Mosk. matem. ob-va, XIV (1965), 3–47