Rings whose additive endomorphisms are n-multiplicative, II

S. Feigelstock

doi:10.1007/BF02454380

Rings whose additive endomorphisms are n-multiplicative, II

S. Feigelstock

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A ring R is called an AE_n -ring, n≥2 a positive integer, if every endomorphism φ{symbol} of additive group of R satisfies φ{symbol}(a₁ a₂... a_n )=φ{symbol}(a₁)φ{symbol}(a₂)...φ{symbol}(a_n ) for all a₁,..., a_n εR. Several results concerning the structure of AE_n -rings are obtained in this note, including an (incomplete) description of AE_n -rings R satisfying R_t R^n-1 ≠0, where R_t is the torsion ideal in R.

Original language	English
Pages (from-to)	21-26
Number of pages	6
Journal	Periodica Mathematica Hungarica
Volume	25
Issue number	1
DOIs	https://doi.org/10.1007/BF02454380
State	Published - Aug 1992

Keywords

AE -rings
Mathematics subject classification numbers: 1991, Primary 20K99, 20K16
Rings
additive endomorphisms

Access to Document

10.1007/BF02454380

Cite this

@article{4d7b3c70bd0e42dd8d45c1b3f3bad5ff,

title = "Rings whose additive endomorphisms are n-multiplicative, II",

abstract = "A ring R is called an AE n -ring, n≥2 a positive integer, if every endomorphism φ\{symbol\} of additive group of R satisfies φ\{symbol\}(a 1 a 2... a n )=φ\{symbol\}(a 1)φ\{symbol\}(a 2)...φ\{symbol\}(a n ) for all a 1,..., a n εR. Several results concerning the structure of AE n -rings are obtained in this note, including an (incomplete) description of AE n -rings R satisfying R t R n-1 ≠0, where R t is the torsion ideal in R.",

keywords = "AE -rings, Mathematics subject classification numbers: 1991, Primary 20K99, 20K16, Rings, additive endomorphisms",

author = "S. Feigelstock",

year = "1992",

month = aug,

doi = "10.1007/BF02454380",

language = "אנגלית",

volume = "25",

pages = "21--26",

journal = "Periodica Mathematica Hungarica",

issn = "0031-5303",

publisher = "Springer Nature",

number = "1",

}

TY - JOUR

T1 - Rings whose additive endomorphisms are n-multiplicative, II

AU - Feigelstock, S.

PY - 1992/8

Y1 - 1992/8

N2 - A ring R is called an AE n -ring, n≥2 a positive integer, if every endomorphism φ{symbol} of additive group of R satisfies φ{symbol}(a 1 a 2... a n )=φ{symbol}(a 1)φ{symbol}(a 2)...φ{symbol}(a n ) for all a 1,..., a n εR. Several results concerning the structure of AE n -rings are obtained in this note, including an (incomplete) description of AE n -rings R satisfying R t R n-1 ≠0, where R t is the torsion ideal in R.

AB - A ring R is called an AE n -ring, n≥2 a positive integer, if every endomorphism φ{symbol} of additive group of R satisfies φ{symbol}(a 1 a 2... a n )=φ{symbol}(a 1)φ{symbol}(a 2)...φ{symbol}(a n ) for all a 1,..., a n εR. Several results concerning the structure of AE n -rings are obtained in this note, including an (incomplete) description of AE n -rings R satisfying R t R n-1 ≠0, where R t is the torsion ideal in R.

KW - AE -rings

KW - Mathematics subject classification numbers: 1991, Primary 20K99, 20K16

KW - Rings

KW - additive endomorphisms

UR - https://www.scopus.com/pages/publications/51649137003

U2 - 10.1007/BF02454380

DO - 10.1007/BF02454380

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:51649137003

SN - 0031-5303

VL - 25

SP - 21

EP - 26

JO - Periodica Mathematica Hungarica

JF - Periodica Mathematica Hungarica

IS - 1

ER -

Rings whose additive endomorphisms are n-multiplicative, II

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this