Geodesic
On graded rings and varieties
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 3, pp. 721-727.

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

For any semigroup $S$, we completely describe all varieties closed for taking $S$-graded rings. Also, we describe all varieties closed for sums of two rings. 
@article{FPM_2002_8_3_a6,
     author = {A. V. Kelarev},
     title = {On graded rings and varieties},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {721--727},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2002_8_3_a6/}
}
TY  - JOUR
AU  - A. V. Kelarev
TI  - On graded rings and varieties
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2002
SP  - 721
EP  - 727
VL  - 8
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2002_8_3_a6/
LA  - ru
ID  - FPM_2002_8_3_a6
ER  - 
%0 Journal Article
%A A. V. Kelarev
%T On graded rings and varieties
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2002
%P 721-727
%V 8
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2002_8_3_a6/
%G ru
%F FPM_2002_8_3_a6
A. V. Kelarev. On graded rings and varieties. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 3, pp. 721-727. http://geodesic.mathdoc.fr/item/FPM_2002_8_3_a6/

[1] Beidar K. I., Mikhalev A. V., “Obobschennye polinomialnye tozhdestva i koltsa, yavlyayuschiesya summami dvukh podkolets”, Algebra i logika, 34:1 (1995), 3–11 | MR | Zbl

[2] Volkov M. V., Kelarev A. V., “Mnogoobraziya i svyazki assotsiativnykh algebr”, Izv. vyssh. uchebn. zaved. Matem., 1986, no. 9, 16–23 | MR | Zbl

[3] Kelarev A. V., “Nedavnie rezultaty i otkrytye voprosy o radikalakh kolets graduirovannykh polugruppami”, Fundam. i prikl. mat., 4:4 (1998), 1115–1139 | MR | Zbl

[4] Klifford A., Preston G., Algebraicheskaya teoriya polugrupp, Mir, M., 1972 | Zbl

[5] Lungu G. B., “O radikalakh polugruppovykh kolets”, Fundam. i prikl. mat., 2:2 (1996), 629–634 | MR | Zbl

[6] Maltsev A. I., “Ob umnozhenii klassov algebraicheskikh sistem”, Sib. mat. zhurn., 8 (1967), 346–365

[7] Pirs R., Assotsiativnye algebry, Mir, M., 1986 | MR

[8] Bahturin Yu. A., Giambruno A., “Identities of sums of commutative subalgebras”, Rend. Circ. Mat. Palermo Ser. 2, 43:2 (1994), 250–258 | DOI | MR | Zbl

[9] Bahturin Yu. A., Kegel O. H., “Lie algebras which are universal sums of abelian subalgebras”, Commun. Algebra, 23 (1995), 2975–2990 | DOI | MR | Zbl

[10] Bahturin Yu. A., Mikhalev A. A., Petrogradsky V. M., Zaicev M. V., Infinite-Dimensional Lie Superalgebras, Berlin, 1992 | Zbl

[11] Evans T., “The lattice of semigroup varieties”, Semigroup Forum, 2 (1971), 1–43 | DOI | MR | Zbl

[12] Ferrero M., Puczyłowski E. R., “On rings which are sums of two subrings”, Arch. Math., 53 (1989), 4–10 | DOI | MR | Zbl

[13] Fukshansky A., “The sum of two locally nilpotent rings may contain a non-commutative free subring”, Proc. Amer. Math. Soc. (to appear)

[14] Gardner B. J., Stewart P. N., “On semi-simple radical classes”, Bull. Austral. Math. Soc., 13 (1975), 349–353 | DOI | MR | Zbl

[15] Howie J. M., Fundamentals of Semigroup Theory, Claredon Press, Oxford, 1995 | MR | Zbl

[16] Kegel O. H., “Zur Nilpotenz gewisser assoziativer Ringe”, Math. Ann., 149 (1963), 258–260 | DOI | MR | Zbl

[17] Kegel O. H., “On rings that are sums of two subrings”, J. Algebra, 1 (1964), 103–109 | DOI | MR | Zbl

[18] Kelarev A. V., “On semigroup graded PI-algebras”, Semigroup Forum., 47 (1993), 294–298 | DOI | MR | Zbl

[19] Kelarev A. V., “A sum of two locally nilpotent rings may be not nil”, Arch. Math., 60 (1993), 431–435 | DOI | MR | Zbl

[20] Kelarev A. V., “Nil properties for rings which are sums of their additive subgroups”, Comm. Algebra, 22 (1994), 5437–5446 | DOI | MR | Zbl

[21] Kelarev A. V., “Applications of epigroups to graded ring theory”, Semigroup Forum, 50 (1995), 327–350 | DOI | MR | Zbl

[22] Kelarev A. V., “On groupoid graded rings”, J. Algebra, 178 (1995), 391–399 | DOI | MR | Zbl

[23] Kelarev A. V., “A primitive ring which is a sum of two Wedderburn radical subrings”, Proc. Amer. Math. Soc., 125 (1997), 2191–2193 | DOI | MR | Zbl

[24] Kelarev A. V., “An answer to a question of Kegel on sums of rings”, Canad. Math. Bull., 41 (1998), 79–80 | DOI | MR | Zbl

[25] Kelarev A. V., McConnell N. R., “Two versions of graded rings”, Publ. Math. (Debrecen), 47:3–4 (1995), 219–227 | MR | Zbl

[26] Kelarev A. V., Plant A., “Bergman's lemma for graded rings”, Comm. Algebra, 23:12 (1995), 4613–4624 | DOI | MR | Zbl

[27] Kepczyk M., Puczyłowski E. R., “On radicals of rings which are sums of two subrings”, Arch. Math., 66 (1996), 8–12 | DOI | MR | Zbl

[28] Kepczyk M., Puczyłowski E. R., “Rings which are sums of two subrings”, J. Pure Appl. Algebra (to appear)

[29] Munn W. D., “A class of band-graded rings”, J. London Math. Soc., 45 (1992), 1–16 | DOI | MR | Zbl

[30] Puczyłowski E. R., “Some questions concerning radicals of associative rings”, Theory of Radicals (Szekszárd, 1991), Coll. Math. Soc. János Bolyai, 61, 1993, 209–227 | MR | Zbl

[31] Stalder S. S., “Gabriel dimension of strong supplementary semilattice sums of rings”, Comm. Algebra, 25 (1997), 1985–2007 | DOI | MR | Zbl