Browse > Article
http://dx.doi.org/10.4134/CKMS.c200341

ON AUTOMORPHISMS IN PRIME RINGS WITH APPLICATIONS  

Raza, Mohd Arif (Department of Mathematics Faculty of Science & Arts-Rabigh King Abdulaziz University)
Publication Information
Communications of the Korean Mathematical Society / v.36, no.4, 2021 , pp. 641-650 More about this Journal
Abstract
The notions of skew-commuting/commuting/semi-commuting/skew-centralizing/semi-centralizing mappings play an important role in ring theory. ${\mathfrak{C}}^*$-algebras with these properties have been studied considerably less and the existing results are motivating the researchers. This article elaborates the structure of prime rings and ${\mathfrak{C}}^*$-algebras satisfying certain functional identities involving automorphisms.
Keywords
Prime ring; automorphism; maximal right ring of quotients; generalized polynomial identity (GPI); ${\mathfrak{C}}^*$-algebra;
Citations & Related Records
연도 인용수 순위
  • Reference
1 N. Krupnik, S. Roch, and B. Silbermann, On C*-algebras generated by idempotents, J. Funct. Anal. 137 (1996), no. 2, 303-319. https://doi.org/10.1006/jfan.1996.0048   DOI
2 C. Lanski and S. Montgomery, Lie structure of prime rings of characteristic 2, Pacific J. Math. 42 (1972), 117-136. http://projecteuclid.org/euclid.pjm/1102968014   DOI
3 P. H. Lee and T. L. Wong, Derivations cocentralizing Lie ideals, Bull. Inst. Math. Acad. Sinica 23 (1995), no. 1, 1-5.
4 C.-K. Liu, An Engel condition with automorphisms for left ideals, J. Algebra Appl. 13 (2014), no. 2, 1350092, 14 pp. https://doi.org/10.1142/S0219498813500928   DOI
5 V. Muller, Nil, nilpotent and PI-algebras, in Functional analysis and operator theory (Warsaw, 1992), 259-265, Banach Center Publ., 30, Polish Acad. Sci. Inst. Math., Warsaw, 1994.
6 G. J. Murphy, C*-Algebras and Operator Theory, Academic Press, Inc., Boston, MA, 1990.
7 M. Nadeem, M. Aslam, and M. A. Javed, On 2-skew commuting mappings of prime rings, Gen. Math. Notes 31 (2015), 1-9.
8 S. Ali, On n-skew-commuting mappings of prime rings with applications to C*-algebras, Proc. Indian Acad. Sci. (Math. Sci), Accepted, 2017.
9 S. Ali, M. Ashraf, M. A. Raza, and A. N. Khan, N-commuting mappings on (semi)-prime rings with applications, Comm. Algebra 47 (2019), no. 5, 2262-2270. https://doi.org/10.1080/00927872.2018.1536203   DOI
10 K. I. Beidar and M. Bresar, Extended Jacobson density theorem for rings with derivations and automorphisms, Israel J. Math. 122 (2001), 317-346. https://doi.org/10.1007/BF02809906   DOI
11 K. I. Beidar, Y. Fong, P. Lee, and T. Wong, On additive maps of prime rings satisfying the Engel condition, Comm. Algebra 25 (1997), no. 12, 3889-3902. https://doi.org/10.1080/00927879708826093   DOI
12 H. E. Bell and J. Lucier, On additive maps and commutativity in rings, Results Math. 36 (1999), no. 1-2, 1-8. https://doi.org/10.1007/BF03322096   DOI
13 H. E. Bell and W. S. Martindale, III, Centralizing mappings of semiprime rings, Canad. Math. Bull. 30 (1987), no. 1, 92-101. https://doi.org/10.4153/CMB-1987-014-x   DOI
14 M. Bresar, On skew-commuting mapping of rings, Bull. Austral. Math. Soc. 41 (1993), 291-296.   DOI
15 C.-L. Chuang, M.-C. Chou, and C.-K. Liu, Skew derivations with annihilating Engel conditions, Publ. Math. Debrecen 68 (2006), no. 1-2, 161-170.   DOI
16 M. Bresar, Centralizing mappings and derivations in prime rings, J. Algebra 156 (1993), no. 2, 385-394. https://doi.org/10.1006/jabr.1993.1080   DOI
17 N. J. Divinsky, On commuting automorphisms of rings, Trans. Roy. Soc. Canada Sect. III 49 (1955), 19-22.
18 B. Davvaz and M. A. Raza, A note on automorphisms of Lie ideals in prime rings, Math. Slovaca 68 (2018), no. 5, 1223-1229. https://doi.org/10.1515/ms-2017-0179   DOI
19 N. Jacobson, Structure of rings, American Mathematical Society Colloquium Publications, Vol. 37. Revised edition, American Mathematical Society, Providence, RI, 1964.
20 J. Vukman, Commuting and centralizing mappings in prime rings, Proc. Amer. Math. Soc. 109 (1990), no. 1, 47-52. https://doi.org/10.2307/2048360   DOI
21 P.-K. Liau and C.-K. Liu, On automorphisms and commutativity in semiprime rings, Canad. Math. Bull. 56 (2013), no. 3, 584-592. https://doi.org/10.4153/CMB-2011-185-5   DOI
22 C.-L. Chuang, Differential identities with automorphisms and antiautomorphisms. I, J. Algebra 149 (1992), no. 2, 371-404. https://doi.org/10.1016/0021-8693(92)90023-F   DOI
23 A. Kaya and C. Koc, Semicentralizing automorphisms of prime rings, Acta Math. Acad. Sci. Hungar. 38 (1981), no. 1-4, 53-55. https://doi.org/10.1007/BF01917518   DOI
24 G. Abrams and M. Tomforde, A class of C*-algebras that are prime but not primitive, Munster J. Math. 7 (2014), no. 2, 489-514. https://doi.org/10.17879/58269761901   DOI
25 A. Najati and M. M. Saem, Skew-commuting mappings on semiprime and prime rings, Hacet. J. Math. Stat. 44 (2015), no. 4, 887-892.
26 M. A. Raza and N. ur Rehman, An identity on automorphisms of Lie ideals in prime rings, Ann. Univ. Ferrara Sez. VII Sci. Mat. 62 (2016), no. 1, 143-150. https://doi.org/10.1007/s11565-016-0240-4   DOI
27 N. Rehman and M. Arif Raza, On m-commuting mappings with skew derivations in prime rings, St. Petersburg Math. J. 27 (2016), no. 4, 641-650; translated from Algebra i Analiz 27 (2015), no. 4, 74-86. https://doi.org/10.1090/spmj/1411   DOI
28 Y. Wang, Power-centralizing automorphisms of Lie ideals in prime rings, Comm. Algebra 34 (2006), no. 2, 609-615. https://doi.org/10.1080/00927870500387812   DOI
29 K. I. Beidar, W. S. Martindale, III, and A. V. Mikhalev, Rings with generalized identities, Monographs and Textbooks in Pure and Applied Mathematics, 196, Marcel Dekker, Inc., New York, 1996.
30 J. Bergen, I. N. Herstein, and J. W. Kerr, Lie ideals and derivations of prime rings, J. Algebra 71 (1981), no. 1, 259-267. https://doi.org/10.1016/0021-8693(81)90120-4   DOI
31 C.-L. Chuang, Differential identities with automorphisms and antiautomorphisms. II, J. Algebra 160 (1993), no. 1, 130-171. https://doi.org/10.1006/jabr.1993.1181   DOI
32 C.-L. Chuang and C.-K. Liu, Extended Jacobson density theorem for rings with skew derivations, Comm. Algebra 35 (2007), no. 4, 1391-1413. https://doi.org/10.1080/00927870601142207   DOI
33 N. Jacobson, PI-algebras, Lecture Notes in Mathematics, Vol. 441, Springer-Verlag, Berlin, 1975.
34 T. S. Erickson, W. S. Martindale, 3rd, and J. M. Osborn, Prime nonassociative algebras, Pacific J. Math. 60 (1975), no. 1, 49-63. http://projecteuclid.org/euclid.pjm/1102868622   DOI
35 M. Fosner, A result concerning additive mappings in semiprime rings, Math. Slovaca 65 (2015), no. 6, 1271-1276. https://doi.org/10.1515/ms-2015-0088   DOI
36 M. Fosner, B. Marcen, and N. Rehman, On skew-commuting mappings in semiprime rings, Math. Slovaca 66 (2016), no. 4, 811-814. https://doi.org/10.1515/ms-2015-0183   DOI
37 M. Ashraf, M. A. Raza, and S. A. Pary, Commutators having idempotent values with automorphisms in semi-prime rings, Math. Rep. (Bucur.) 20(70) (2018), no. 1, 51-57.
38 A. Kaya, A theorem on semicentralizing derivations of prime rings, Math. J. Okayama Univ. 27 (1985), 11-12.