The $(j,m)$-core inverse in rings with involution

Sanzhang Xu; Jianlong Chen; Dijana Mosić

doi:10.15672/hujms.701870

Araştırma Makalesi

Yıl 2020, Cilt: 49 Sayı: 5, 1676 - 1685, 06.10.2020

Sanzhang Xu Jianlong Chen Dijana Mosić

https://doi.org/10.15672/hujms.701870

Öz

Kaynakça

[1] O.M. Baksalary and G. Trenkler. Core inverse of matrices, Linear Multilinear Algebra, 58(6), 681–697, 2010.
[2] O.M. Baksalary and G. Trenkler, On a generalized core inverse, Appl. Math. Comput. 236, 450–457, 2014.
[3] M.P. Drazin, Pseudo-inverses in associative rings and semigroup, Amer. Math. Monthly, 65, 506–514, 1958.
[4] R.E. Hartwig, Block generalized inverses, Arch. Retional Mech. Anal. 61(3), 197–251, 1976.
[5] S.B. Malik and N. Thome, On a new generalized inverse for matrices of an arbitrary index, Appl. Math. Comput. 226, 575–580, 2014.
[6] D. Mosić and D.S. Djordjević, Moore-Penrose-invertible normal and Hermitian elements in rings, Linear Algebra Appl. 431, 732–745, 2009.
[7] P. Patrício and R. Puystjens, Drazin-Moore-Penrose invertiblity in rings, Linear Algebra Appl. 389, 159–173, 2004.
[8] D.S. Rakić, N.Č. Dinčić and D.S. Djordjević, Group, Moore-Penrose, core and dual core inverse in rings with involution, Linear Algebra Appl. 463, 115–133, 2014.
[9] H. Schwerdtfeger, Introduction to Linear Algebra and the Theory of Matrices, P. Noordhoff, Groningen, 1950.
[10] J. von Neumann, On regular rings, Proc. Nati. Acad. Sci. U.S.A. 22 (12), 707–713, 1936.
[11] H.X. Wang and X.J. Liu, A partial order on the set of complex matrices with index one, Linear Multilinear Algebra, 66 (1), 206–216, 2018.
[12] S.Z. Xu, J.L. Chen and J. Benítez, EP elements in rings with involution, Bull. Malays. Math. Sci. Soc. 42, 3409–3426, 2019.
[13] S.Z. Xu, J.L. Chen, J. Benítez and D.G. Wang, Generalized core inverse of matrices, Miskolc Math. Notes, 20 (1), 565–584, 2019.
[14] S.Z. Xu, J.L. Chen and X.X. Zhang, New characterizations for core and dual core inverses in rings with involution, Front. Math. China. 12 (1), 231–246, 2017.

The $(j,m)$-core inverse in rings with involution

Yıl 2020, Cilt: 49 Sayı: 5, 1676 - 1685, 06.10.2020

Sanzhang Xu Jianlong Chen Dijana Mosić

https://doi.org/10.15672/hujms.701870

Öz

Let $R$ be a unital ring with involution. The $(j,m)$-core inverse of a complex matrix was extended to an element in $R$. New necessary and sufficient conditions such that an element in $R$ to be $(j,m)$-core invertible are given. Moreover, several additive and product properties of two $(j,m)$-core invertible elements are investigated and a order related to the $(j,m)$-core inverse is introduced.

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Anahtar Kelimeler

Moore-Penrose inverse, (j-m) core inverse, EP element

Kaynakça

[1] O.M. Baksalary and G. Trenkler. Core inverse of matrices, Linear Multilinear Algebra, 58(6), 681–697, 2010.
[2] O.M. Baksalary and G. Trenkler, On a generalized core inverse, Appl. Math. Comput. 236, 450–457, 2014.
[3] M.P. Drazin, Pseudo-inverses in associative rings and semigroup, Amer. Math. Monthly, 65, 506–514, 1958.
[4] R.E. Hartwig, Block generalized inverses, Arch. Retional Mech. Anal. 61(3), 197–251, 1976.
[5] S.B. Malik and N. Thome, On a new generalized inverse for matrices of an arbitrary index, Appl. Math. Comput. 226, 575–580, 2014.
[6] D. Mosić and D.S. Djordjević, Moore-Penrose-invertible normal and Hermitian elements in rings, Linear Algebra Appl. 431, 732–745, 2009.
[7] P. Patrício and R. Puystjens, Drazin-Moore-Penrose invertiblity in rings, Linear Algebra Appl. 389, 159–173, 2004.
[8] D.S. Rakić, N.Č. Dinčić and D.S. Djordjević, Group, Moore-Penrose, core and dual core inverse in rings with involution, Linear Algebra Appl. 463, 115–133, 2014.
[9] H. Schwerdtfeger, Introduction to Linear Algebra and the Theory of Matrices, P. Noordhoff, Groningen, 1950.
[10] J. von Neumann, On regular rings, Proc. Nati. Acad. Sci. U.S.A. 22 (12), 707–713, 1936.
[11] H.X. Wang and X.J. Liu, A partial order on the set of complex matrices with index one, Linear Multilinear Algebra, 66 (1), 206–216, 2018.
[12] S.Z. Xu, J.L. Chen and J. Benítez, EP elements in rings with involution, Bull. Malays. Math. Sci. Soc. 42, 3409–3426, 2019.
[13] S.Z. Xu, J.L. Chen, J. Benítez and D.G. Wang, Generalized core inverse of matrices, Miskolc Math. Notes, 20 (1), 565–584, 2019.
[14] S.Z. Xu, J.L. Chen and X.X. Zhang, New characterizations for core and dual core inverses in rings with involution, Front. Math. China. 12 (1), 231–246, 2017.

Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Matematik
Yazarlar	Sanzhang Xu 0000-0002-9744-477X Jianlong Chen 0000-0002-6798-488X Dijana Mosić 0000-0002-3255-9322
Yayımlanma Tarihi	6 Ekim 2020
Yayımlandığı Sayı	Yıl 2020 Cilt: 49 Sayı: 5

Kaynak Göster

APA	Xu, S., Chen, J., & Mosić, D. (2020). The $(j,m)$-core inverse in rings with involution. Hacettepe Journal of Mathematics and Statistics, 49(5), 1676-1685. https://doi.org/10.15672/hujms.701870
AMA	Xu S, Chen J, Mosić D. The $(j,m)$-core inverse in rings with involution. Hacettepe Journal of Mathematics and Statistics. Ekim 2020;49(5):1676-1685. doi:10.15672/hujms.701870
Chicago	Xu, Sanzhang, Jianlong Chen, ve Dijana Mosić. “The $(j,m)$-Core Inverse in Rings With Involution”. Hacettepe Journal of Mathematics and Statistics 49, sy. 5 (Ekim 2020): 1676-85. https://doi.org/10.15672/hujms.701870.
EndNote	Xu S, Chen J, Mosić D (01 Ekim 2020) The $(j,m)$-core inverse in rings with involution. Hacettepe Journal of Mathematics and Statistics 49 5 1676–1685.
IEEE	S. Xu, J. Chen, ve D. Mosić, “The $(j,m)$-core inverse in rings with involution”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 5, ss. 1676–1685, 2020, doi: 10.15672/hujms.701870.
ISNAD	Xu, Sanzhang vd. “The $(j,m)$-Core Inverse in Rings With Involution”. Hacettepe Journal of Mathematics and Statistics 49/5 (Ekim 2020), 1676-1685. https://doi.org/10.15672/hujms.701870.
JAMA	Xu S, Chen J, Mosić D. The $(j,m)$-core inverse in rings with involution. Hacettepe Journal of Mathematics and Statistics. 2020;49:1676–1685.
MLA	Xu, Sanzhang vd. “The $(j,m)$-Core Inverse in Rings With Involution”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 5, 2020, ss. 1676-85, doi:10.15672/hujms.701870.
Vancouver	Xu S, Chen J, Mosić D. The $(j,m)$-core inverse in rings with involution. Hacettepe Journal of Mathematics and Statistics. 2020;49(5):1676-85.