On Hirano inverses in rings

Huanyin CHEN; Marjan Sheibani ABDOLYOUSEFI

Makale detayları

On Hirano inverses in rings

Yazarlar:

Huanyin CHEN | Marjan Sheibani ABDOLYOUSEFI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 4, pp.2049-2057

Belge Tipi:

Makale

Yayın Tarihi:

7/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000745579

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

We completely characterize a subclass of Drazin inverses by means of tripotents and nilpotents. We prove that an element aaa in a ring RRR has Hirano inverse if and only if a2∈Ra2∈Ra^2\in R has strongly Drazin inverse, if and only if a−a3a−a3a-a^3 is nilpotent. If 12∈R12∈R\frac{1}{2}\in R, we prove that a∈Ra∈Ra\in R has Hirano inverse if and only if there exists p3=p∈comm2(a)p3=p∈comm2(a)p^3=p\in comm^2(a) such that a−p∈N(R)a−p∈N(R)a-p\in N(R), if and only if there exist two idempotents e,f∈comm2(a)e,f∈comm2(a)e,f\in comm^2(a) such that a+e−f∈N(R)a+e−f∈N(R)a+e-f\in N(R). Multiplicative and additive results for this generalized inverse are thereby obtained.

Makale detayları

On Hirano inverses in rings

Yazarlar: Huanyin CHEN | Marjan Sheibani ABDOLYOUSEFI

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2019 Vol.43 Issue 4, pp.2049-2057

Belge Tipi: Makale

Yayın Tarihi: 7/2019

Belge Dili: İngilizce

Document ID (Org No.): 2000745579

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Huanyin CHEN | Marjan Sheibani ABDOLYOUSEFI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 4, pp.2049-2057

Belge Tipi:

Makale

Yayın Tarihi:

7/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000745579

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098