|
|
|
|
Литература
|
|
| |
| 1. |
A. Abdollahi, “Commuting graphs of full matrix rings over finite fields”, Linear Algebra Appl., 428 (2008), 2947–2954     |
| 2. |
A. Abdollahi, S. Akbari, H. R. Maimani, “Non-commuting graph of a group”, J. Algebra, 298:2 (2006), 468–492 |
| 3. |
S. Akbari, H. Bidkhori, A. Mohammadian, “Commuting graphs of matrix algebras”, Commun. Algebra, 36 (2008), 4020–4031 |
| 4. |
S. Akbari, M. Ghandehari, M. Hadian, A. Mohammadian, “On commuting graphs of semisimple rings”, Linear Algebra Appl., 390 (2004), 345–355 |
| 5. |
S. Akbari, H. R. Maimani, S. Yassemi, “When zero-divisor graph is planar or a complete $r$-partite graph”, J. Algebra, 270 (2003), 169–180 |
| 6. |
S. Akbari, A. Mohammadian, “On the zero-divisor graph of a commutative ring”, J. Algebra, 274 (2004), 847–855 |
| 7. |
S. Akbari, A. Mohammadian, “Zero-divisor graphs of non-commutative rings”, J. Algebra, 296 (2006), 462–479 |
| 8. |
S. Akbari, A. Mohammadian, “On zero-divisor graphs of finite rings”, J. Algebra, 314 (2007), 168–184 |
| 9. |
S. Akbari, A. Mohammadian, H. Radjavi, P. Raja, “On the diameters of commuting graphs”, Linear Algebra Appl., 418 (2006), 161–176 |
| 10. |
S. Akbari, P. Raja, “Commuting graphs of some subsets in simple rings”, Linear Algebra Appl., 416 (2006), 1038–1047 |
| 11. |
D. F. Anderson, A. Frazier, A. Lauve, P. S. Livingston, “The zero-divisor graph of a commutative ring. II”, Lect. Notes Pure Appl. Math., 220, Marcel Dekker, New York, 2001, 61–72 |
| 12. |
D. F. Anderson, R. Levy, J. Shapiro, “Zero-divisor graphs, von Neumann regular rings, and Boolean algebras”, J. Pure Appl. Algebra, 180:3 (2003), 221–241 |
| 13. |
D. F. Anderson, P. S. Livingston, “The zero-divisor graph of a commutative ring”, J. Algebra, 217 (1999), 434–447 |
| 14. |
М. Атья, И. Макдональд, Введение в коммутативную алгебру, Мир, М., 1972 |
| 15. |
J. K. Baksalary, J. Hauke, “A further algebraic version of Cochran's theorem and matrix partial orderings”, Linear Algebra Appl., 127 (1990), 157–169 |
| 16. |
I. Beck, “Coloring of Commutative Rings”, J. Algebra, 116 (1988), 208–226 |
| 17. |
G. Dolinar, B. Kuzma, P. Oblak, “On maximal distances in a commuting graph”, Electron. J. Linear Algebra, 23 (2012), 243–256 |
| 18. |
G. Dolinar, A. E. Guterman, B. Kuzma, P. Oblak, “Commuting graphs and extremal centralizers”, Ars Math. Contemp., 7:2 (2014), 453–459 |
| 19. |
G. Dolinar, A. E. Guterman, B. Kuzma, P. Oblak, “Extremal matrix centralizers”, Linear Algebra Appl., 438:7 (2013), 2904–2910 |
| 20. |
D. Dolzan, P. Oblak, “Commuting graph of matrices over semirings”, Linear Algebra Appl., 435 (2011), 1657–1665 |
| 21. |
Ф. Харари, Теория графов, Мир, М., 1973 |
| 22. |
I. N. Herstein, Topics in Algebra, 2-nd edition, Wiley, 1975 |
| 23. |
M. Giudici, A. Pope, “The diameters of commuting graphs of linear groups and matrix rings over the integers modulo $m$”, Australasian J. Combinatorics, 48 (2010), 221–230 |
| 24. |
L. C. Grove, Algebra, AP, New York, 1980 |
| 25. |
А. Э. Гутерман, М. А. Ефимов, “Монотонные отображения матриц индекса 1”, Зап. научн. семин. ПОМИ, 405, 2012, 67–96  |
| 26. |
A. Iranmanesh, A. Jafarzadeh, “On the commuting graph associated with the symmetric and alternating groups”, J. Alg. Appl., 7 (2008), 129–146 |
| 27. |
D. C. Kleinecke, “On operator commutators”, Proc. Amer. Math. Soc., 8 (1957), 535–536 |
| 28. |
T. G. Lucas, “The diameter of a zero divisor graph”, J. Algebra, 301 (2006), 174–193 |
| 29. |
A. R. Moghaddamfar, “About noncommuting graphs”, J. Sib. Math., 47:5 (2006), 911–914 |
| 30. |
A. Mohammadian, “On commuting graphs of finite matrix rings”, Commun. Algebra, 38 (2010), 988–994 |
| 31. |
P. G. Ovchinnikov, “Automorphisms of the poset of skew projections”, J. Funct. Analysis, 115 (1993), 184–189 |
| 32. |
Ф. В. Широков, “Доказательство гипотезы Капланского”, Усп. матем. наук, 11:4(70) (1956), 167–168 |
| 33. |
Д. А. Супруненко, Р. А. Тышкевич, Перестановочные матрицы, Наука и Техника, Минск, 1966 |
| 34. |
P. Šemrl, “Order-preserving maps on the poset of idempotent matrices”, Acta Sci. Math. (Szeged), 69 (2003), 481–490 |
| 35. |
O. Taussky, “Commutativity of finite matrices”, Amer. Math. Monthly, 64 (1957), 239–255 |
| 36. |
J. H. M. Wedderburn, Lectures on Matrices, Amer. Math. Society Colloquium Publications, 17, 1934 |
