半环上保持矩阵{1}-逆的线性算子Linear operators preserving {1}-inverses of matrices over semirings
李栋梁;任苗苗;刘建华;李斌;
摘要(Abstract)：
刻画了某类特殊可换无零因子反环上保持矩阵{1}-逆的可逆线性算子,并将此结果推广到此类无零因子反环的任意直积上.推广了某些文献的一些结果.
关键词(KeyWords)： 可换无零因子反环;{1}-逆;线性算子
基金项目(Foundation): 陕西省自然科学专项基金(2011JQ1017)
作者(Authors): 李栋梁;任苗苗;刘建华;李斌;
参考文献(References)：
- [1]Song S Z,Kang K T,Beasley L B.Idempotent matrix preservers over Boolean algebras[J].J.Korean Math.Soc.,2007,44(1):169-178.
- [2]Rao P S S N V P,Rao K P S B.On generalized inverses of Boolean matrices[J].Linear Algebra Appl.,1975,11:135-153.
- [3]Frobenius G.Uber Die Drastellung Der Endlichen Grouppen Durch Lineare Substitutionen[M].Berlin:Sitzungsber.Preuss.Akad.Wiss.,1897.
- [4]Marcus M.Linear transformations on matrices[J].J.Res.Nat.Bur.Standards,1971,75B:107-113.
- [5]卜长江,郝立丽.保矩阵{1}逆的线性映射[J].数学研究,2003,36(4):418-421.
- [6]Bu C J.Invertible linear maps preserving{1}-inverses of matrices over PID[J].J.Appl.Math.Computing,2006,22(3):255-265.
- [7]Chan C H,Lim M H.Linear transformations on symmetric matrices that preserve commutativity[J].Linear Algebra Appl.,1982,47:11-22.
- [8]Chan G H,Lim M H,Tan K K.Linear preservers on matrices[J].Linear Algebra Appl.,1987,93:67-80.
- [9]Choi M D,Jafarian A A,Radjavi H.Linear maps preserving commutativity[J].Linear Algebra Appl.,1976,87:227-241.
- [10]DolZˇan D,Oblak P.Idempotent matrices over antirings[J].Linear Algebra Appl.,2009,431(5/6/7):823-832.
- [11]任苗苗,邵勇,赵宪钟.保持半环上矩阵{1}-逆的线性算子[J].西北大学学报:自然科学版,2012,42(1):7-11.
- [12]任苗苗.几类保持半环上矩阵不变量的线性算子[D].西安:西北大学数学系,2012.
- [13]张显,曹重光.关于域上矩阵广义逆的加法映射[J].数学学报,2004,47(5):1013-1018.