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2015 | 13 | 1 |
Tytuł artykułu

Solutions of minus partial ordering equations over von Neumann regular rings

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we mainly derive the general solutions of two systems of minus partial ordering equations over von Neumann regular rings. Meanwhile, some special cases are correspondingly presented. As applications, we give some necessary and sufficient conditions for the existence of solutions. It can be seen that some known results can be regarded as the special cases of this paper.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2014-03-04
zaakceptowano
2015-01-07
online
2015-02-06
Twórcy
autor
  • Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444, P.R. China
autor
  • Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444, P.R. China
Bibliografia
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  • [3] J.K. Baksalary, S. Puntanen, Characterizations of the best linear unbiased estimator in the general Gauss–Markov model with theuse of matrix partial orderings, Linear Algebra Appl. 127 (1990), 363–370.
  • [4] J.K. Baksalary, F. Pukelsheim, G.P.H. Styan, Some properties of matrix partial orderings, Linear Algebra Appl. 119 (1989), 57–85.
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  • [6] B. Blackwood, S.K. Jain, K.M. Prasad, A.K. Srivastava, Shorted operators relative to a partial order in a regular ring, Commun.Algebra 37 (2009), 4141–4152.[WoS]
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  • [10] K.R. Goodearl, von Neumann Regular Rings, 2nd edn. Krieger, Florida (1991).
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  • [15] N. Jacobson, Basic Algebra II, 2nd edn. Freeman, New York (1989).
  • [16] S.K. Jain, S.K. Mitra, H.J. Werner, Extensions of G-based matrix partial orders, Siam J. Matrix Anal. Appl. 17(4) (1996), 834–850.[Crossref]
  • [17] P. Legiša, Automorphisms ofMn, partially ordered by rank subtractivity ordering, Linear Algebra Appl. 389 (2004), 147–158.
  • [18] G. Marsaglia, G.P.H. Styan, Equalities and inequalities for ranks of matrices, Linear Multilinear Algebra 2 (1974), 269–292.[Crossref]
  • [19] S.K. Mitra, The minus partial order and the shorted matrix, Linear Algebra Appl. 83 (1986), 1–27.
  • [20] S.K. Mitra, M.L. Puri, Shorted matrices-an extended concept and some applications, Linear Algebra Appl. 42 (1982), 57–79.
  • [21] S.K. Mitra, Matrix partial orders through generalized inverses unified theory, Linear Algebra Appl. 148 (1991), 237–263.[WoS]
  • [22] K.S.S. Nambooripad, The natural partial order on a regular semigroup. Proc. Edinb. Math. Soc. 23 (1980), 249–260.[Crossref]
  • [23] R. Penrose, A generalized inverse for matrices. Proc. Camb. Philos. Soc. 51 (1955), 406–413.
  • [24] Y. Tian, Solving a minus partial ordering equation over von Neumann regular rings, Revista mathematica complutense. 24(2)(2011), 335-342.[WoS]
  • [25] Q.W. Wang, A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity, Linear AlgebraAppl. 384 (2004) 43-54.
  • [26] H.J. Werner, Generalized inversion and weak bi-complementarity, Linear and Multilinear Algebra 19 (1986), 357–372.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0022
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