Involution rings with unique minimal *-biideal
Algebra and discrete mathematics, Tome 21 (2016) no. 2, pp. 255-263.

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

The structure of certain involution rings which have exactly one minimal *-biideal is determined. In addition, involution rings with identity having a unique maximal biideal are characterized.
Keywords: involution, biideal, nilpotent ring, local ring, subdirectly irreducible ring, Jacobson radical.
@article{ADM_2016_21_2_a6,
     author = {D. I. C. Mendes},
     title = {Involution rings with unique minimal *-biideal},
     journal = {Algebra and discrete mathematics},
     pages = {255--263},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2016_21_2_a6/}
}
TY  - JOUR
AU  - D. I. C. Mendes
TI  - Involution rings with unique minimal *-biideal
JO  - Algebra and discrete mathematics
PY  - 2016
SP  - 255
EP  - 263
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2016_21_2_a6/
LA  - en
ID  - ADM_2016_21_2_a6
ER  - 
%0 Journal Article
%A D. I. C. Mendes
%T Involution rings with unique minimal *-biideal
%J Algebra and discrete mathematics
%D 2016
%P 255-263
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2016_21_2_a6/
%G en
%F ADM_2016_21_2_a6
D. I. C. Mendes. Involution rings with unique minimal *-biideal. Algebra and discrete mathematics, Tome 21 (2016) no. 2, pp. 255-263. http://geodesic.mathdoc.fr/item/ADM_2016_21_2_a6/

[1] Aburawash U. A., “On *-simple involution rings with minimal $*$-biideals”, Studia Sci. Math. Hungar., 32 (1996), 455–458 | MR | Zbl

[2] Aburawash U. A., “On involution rings”, East-West J. Math., 2:2 (2000), 109–126 | MR | Zbl

[3] Aburawash U. A., “On $*$-minimal $*$-ideals and $*$-biideals in involution rings”, Acta Math. Hungar., 129:4 (2010), 297–302 | DOI | MR | Zbl

[4] Beidar K. I. and Wiegandt R., “Rings with involution and chain conditions”, J. Pure Appl. Algebra, 87 (1993), 205–220 | DOI | MR | Zbl

[5] Birkenmeier G. F., Groenewald N. J. and Heatherly H. E., “Minimal and maximal ideals in rings with involution”, Beitr. Algebra Geom., 38:2 (1997), 217–225 | MR | Zbl

[6] Desphande M. G., “Structure of right subdirectly irreducible rings I”, J. Algebra, 17 (1971), 317–325 | DOI | MR

[7] Desphande M. G., “Structure of right subdirectly irreducible rings II”, Pacific J. Math., 42:1 (1972), 39–44 | DOI | MR

[8] Heatherly H. E., Lee E. K. S and Wiegandt R., “Involutions on universal algebras”, Nearrings, Nearfields and $K$-loops, Kluwer, 1997, 269–282 | DOI | MR | Zbl

[9] Loi N. V., “On the structure of semiprime involution rings”, General Algebra, Proc. Krems Conf. 1988, North-Holland, Amsterdam, 1990, 153–161 | MR

[10] Loi N. V. and Wiegandt R., “On involution rings with minimum condition”, Ring Theory, Israel Math. Conf. Proc., v. 1, 1989, 203–214 | MR

[11] Mendes D. I. C., “On $*$-essential ideals and biideals of rings with involution”, Quaest. Math., 26 (2003), 67–72 | DOI | MR | Zbl

[12] Mendes D. I. C., “Minimal $*$-biideals of involution rings”, Acta Sci. Math. (Szeged), 75 (2009), 487–491 | MR | Zbl