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Combinatorial methods in algebra. Transl. from the Russian. (English) Zbl 1093.13500

The articles of this volume are translations of the journal “Fundam. Prikl. Mat. 9, No. 3 (Russian)(2003)” and will be reviewed individually together with the Russian original.

MSC:

13-06 Proceedings, conferences, collections, etc. pertaining to commutative algebra
17-06 Proceedings, conferences, collections, etc. pertaining to nonassociative rings and algebras
20-06 Proceedings, conferences, collections, etc. pertaining to group theory
00B15 Collections of articles of miscellaneous specific interest
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References:

[1] A. Alieva and A. Guterman, ”Monotone linear transformations on matrices are invertible,” Comm. Algebra, to appear. · Zbl 1082.15002
[2] J. K. Baksalary and J. Hauke, ”Partial orderings on matrices referring to singular values or eigenvalues,” Linear Algebra Appl., 96, 17–26 (1987). · Zbl 0627.15005 · doi:10.1016/0024-3795(87)90333-8
[3] J. K. Baksalary and J. Hauke, ”A further algebraic version of Cochran’s theorem and matrix partial orderings,” Linear Algebra Appl., 127, 157–169 (1990). · Zbl 0696.15005 · doi:10.1016/0024-3795(90)90341-9
[4] J. K. Baksalary and S. K. Mitra, ”Left-star and right-star partial orderings,” Linear Algebra Appl., 149, 73–89 (1991). · Zbl 0717.15004 · doi:10.1016/0024-3795(91)90326-R
[5] J. K. Baksalary, F. Pukelsheim, and G. P. H. Styan, ”Some properties of matrix partial orderings,” Linear Algebra Appl., 119, 57–85 (1989). · Zbl 0681.15005 · doi:10.1016/0024-3795(89)90069-4
[6] M. P. Drazin, ”Natural structures on semigroups with involution,” Bull. Amer. Math. Soc., 84, No. 1, 139–141 (1978). · Zbl 0395.20044 · doi:10.1090/S0002-9904-1978-14442-5
[7] J. Groß, ”A note on rank-subtractivity ordering,” Linear Algebra Appl., 289, 151–160 (1999). · Zbl 0941.15011 · doi:10.1016/S0024-3795(98)10236-7
[8] R. E. Hartwig, ”How to partially order regular elements,” Math. Japon., 25, No. 1, 1–13 (1980). · Zbl 0442.06006
[9] J. Hauke, A. Markiewicz, and T. Szulc, ”Inter-and extrapolatory properties of matrix partial orderings,” Linear Algebra Appl., 332–334, 437–445 (2001). · Zbl 0982.15027 · doi:10.1016/S0024-3795(01)00294-4
[10] C.-K. Li and N.-K. Tsing, ”Linear preserver problems: A brief introduction and some special techniques,” Linear Algebra Appl., 162–164, 217–235 (1992). · Zbl 0762.15016 · doi:10.1016/0024-3795(92)90377-M
[11] K. S. S. Nambooripad, ”The natural partial order on a regular semigroup,” Proc. Edinburgh Math. Soc., 23, 249–260 (1980). · Zbl 0459.20054 · doi:10.1017/S0013091500003801
[12] S. Pierce et al., ”A survey of linear preserver problems,” Linear and Multilinear Algebra, 33, 1–119 (1992). · Zbl 0767.15006
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