On rings determined by their idempotents and units

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10471834" target="_blank" >RIV/00216208:11320/23:10471834 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=satbwW_OJ2" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=satbwW_OJ2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1080/00927872.2023.2173762" target="_blank" >10.1080/00927872.2023.2173762</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On rings determined by their idempotents and units

Popis výsledku v původním jazyce

This paper describes properties of three certain classes of rings determined by conditions on idempotents and units, namely, the condition that any two generators of each principal right ideal are associated (UG rings), the condition that every principal right ideal is generated by a sum of a unit and an idempotent (Pr ), and the condition xy = 0 implies xsy = 0 for a sum of idempotent and unit s and any elements x, y of a ring (idun-semicommutative rings). It is proved that the class of all UG rings contains every local as well as every von Neumann regular ring, and the condition Pr is satisfied by both semiperfect and regular rings. Both local and abelian regular rings are proved to be necessarily idun-semicommutative. For all three classes are presented some closure properties and illustrating examples.

Název v anglickém jazyce

On rings determined by their idempotents and units

Popis výsledku anglicky

This paper describes properties of three certain classes of rings determined by conditions on idempotents and units, namely, the condition that any two generators of each principal right ideal are associated (UG rings), the condition that every principal right ideal is generated by a sum of a unit and an idempotent (Pr ), and the condition xy = 0 implies xsy = 0 for a sum of idempotent and unit s and any elements x, y of a ring (idun-semicommutative rings). It is proved that the class of all UG rings contains every local as well as every von Neumann regular ring, and the condition Pr is satisfied by both semiperfect and regular rings. Both local and abelian regular rings are proved to be necessarily idun-semicommutative. For all three classes are presented some closure properties and illustrating examples.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Communications in Algebra

ISSN

0092-7872

e-ISSN

1532-4125

Svazek periodika

51

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

—

Kód UT WoS článku

000923959800001

EID výsledku v databázi Scopus

2-s2.0-85147666901