A Note on Additive Groups of Some Specific Associative Rings

• Autorzy: Mateusz Woronowicz
• Języki publikacji: EN

Abstrakty

EN

Almost complete description of abelian groups (A, +, 0) such that every associative ring R with the additive group A satisfies the condition: every subgroup of A is an ideal of R, is given. Some new results for SR-groups in the case of associative rings are also achieved. The characterization of abelian torsion-free groups of rank one and their direct sums which are not nil-groups is complemented using only elementary methods.(original abstract)

Słowa kluczowe

PL

Matematyka; Algebra; Teoria grup

EN

Mathematics; Algebra; Groups theory

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2016
• Tom: 30
• Strony: 219-229

Twórcy

autor

Mateusz Woronowicz

• University of Bialystok, Poland

Bibliografia

• Aghdam A.M.,Square subgroup of an Abelian group, Acta. Sci. Math.51(1987), 343-348.
• Aghdam A.M., Karimi F., Najafizadeh A.,On the subgroups of torsion-free groupswhich are subrings in every ring, Ital. J. Pure Appl. Math.31(2013), 63-76.
• Aghdam A.M., Najafizadeh A.,Square submodule of a module, Mediterr. J. Math.7(2010), no. 2, 195-207.
• Andruszkiewicz R.R., Woronowicz M.,On associative ring multiplication on abelianmixed groups, Comm. Algebra42(2014), no. 9, 3760-3767.
• Andruszkiewicz R.R., Woronowicz M.,OnSI-groups, Bull. Aust. Math. Soc.91(2015),92-103.
• Chekhlov A.R.,On abelian groups, in which all subgroups are ideals, Vestn. Tomsk.Gos. Univ. Mat. Mekh. (2009), no. 3(7), 64-67.
• Feigelstock S., Additive groups of rings. Vol. I, Pitman Advanced Publishing Program, Boston, 1983.
• Feigelstock S., Additive groups of rings whose subrings are ideals, Bull. Austral. Math. Soc. 55 (1997), 477-481.
• Feigelstock S., Rings in which a power of each element is an integral multiple of the element, Archiv der Math.32 (1979), 101-103.
• Fuchs L., Infinite abelian groups. Vol. I, Academic Press, New York-London, 1970.
• Fuchs L., Infinite abelian groups. Vol. II, Academic Press, New York-London, 1973.
• Kompantseva E.I., Absolute nil-ideals of Abelian groups, Fundam. Prikl. Mat. 17 (2012), no. 8, 63-76.
• Kompantseva E.I., Abelian dqt-groups and rings on them, Fundam. Prikl. Mat. 18 (2013), no. 3, 53-67.
• O'Neill J.D., Rings whose additive subgroup are subrings, Pacific J. Math. 66 (1976), no. 2, 509-522.
• Pham Thi Thu Thuy, Torsion abelian RAI-groups, J. Math. Sci. (N. Y.) 197 (2014), no. 5, 658-678.
• Pham Thi Thu Thuy, Torsion abelian afi-groups, J. Math. Sci. (N. Y.) 197 (2014), no. 5, 679-683.

Identyfikatory

DOI

10.1515/amsil-2015-0013