Mixed idempotent Abelian groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 5, pp. 153-157
An Abelian group is called idempotent if any element is idempotent for some multiplication. This paper contains a complete description of torsion-free idempotent groups and periodic idempotent groups. We also give a description of mixed idempotent groups.
@article{FPM_2019_22_5_a15,
author = {A. G. Tisovsky},
title = {Mixed idempotent {Abelian} groups},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {153--157},
year = {2019},
volume = {22},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2019_22_5_a15/}
}
A. G. Tisovsky. Mixed idempotent Abelian groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 5, pp. 153-157. http://geodesic.mathdoc.fr/item/FPM_2019_22_5_a15/
[1] Krylov P. A., “Smeshannye abelevy gruppy kak moduli nad svoimi koltsami endomorfizmov”, Fundament. i prikl. matem., 6:3 (2000), 793–812 | MR | Zbl
[2] Krylov P. A., “Nasledstvennye koltsa endomorfizmov smeshannykh abelevykh grupp”, Sib. matem. zhurn., 43:1 (2002), 108–119 | MR | Zbl
[3] Fuks L., Beskonechnye abelevy gruppy, v. 1, 2, Mir, M., 1974
[4] Arnold D. M., Finite Rank Torsion Free Abelian Groups and Rings, Springer, Berlin, 1982 | MR | Zbl
[5] Beaumont R., “Rings with additive group which is the direct sum of cyclic groups”, Duke Math. J., 15 (1948), 367–369 | DOI | MR | Zbl
[6] Szele T., “Zur Theorie der Zeroringe”, Math. Ann., 121 (1949), 242–246 | DOI | MR | Zbl