A characterization of weakly J(n)-rings

• Autorzy: Danchev P. V.

Identyfikatory

DOI

10.7862/rf.2018.5

• Języki publikacji: EN

Abstrakty

EN

A ring R is called a J(n)-ring if there exists a natural number n ≥ 1 such that for each element r ∈ R the equality r (n+1) = r holds and a weakly J(n)-ring if there exists a natural number n ≥ 1 such that for each element r ∈ R the equalities r (n+1) = r or r(n+1) = -r hold. We completely describe both classes of these rings R for any n, thus considerably extending some well-known results in the subject, especially that of V. Perić in Publ. Inst. Math. Beograd (1983) as well as, in particular, the classical description of Boolean rings when n = 1.

Słowa kluczowe

EN

Boolean rings; idempotents; units; nilpotents; Jacobson radical; J (n)-rings

PL

pierścień Boole'a; idempotent pierścienia; element idempotentny; jednostki; nilpotent pierścienia; element nilpotentny; rodnik Jacobsona

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2018
• Tom: Vol. 41
• Strony: 53--61
• Opis fizyczny: Bibliogr. 17 poz..

Twórcy

autor

Danchev P. V.

• Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, "Acad. G. Bonchev" str., bl. 8, 1113 Sofia, Bulgaria

Bibliografia

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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).