Research article

Some differential identities of MA-semirings with involution

  • Received: 14 September 2020 Accepted: 02 November 2020 Published: 16 December 2020
  • MSC : 16Y60, 16W10

  • In this paper, we discuss some differential identities of MA-semirings with involution. The aim to study these identities is to induce commutativity in MA-semirings.

    Citation: Liaqat Ali, Yaqoub Ahmed Khan, A. A. Mousa, S. Abdel-Khalek, Ghulam Farid. Some differential identities of MA-semirings with involution[J]. AIMS Mathematics, 2021, 6(3): 2304-2314. doi: 10.3934/math.2021139

    Related Papers:

  • In this paper, we discuss some differential identities of MA-semirings with involution. The aim to study these identities is to induce commutativity in MA-semirings.



    加载中


    [1] M. A. Javed, M. Aslam, M. Hussain, On condition (A2) of Bandlet and Petrich for inverse semiqrings, Int. Math. Forum, 7 (2012), 2903–2914.
    [2] H. J. Bandlet, M. Petrich, Subdirect products of rings and distrbutive lattics, Proc. Edin. Math. Soc., 25 (1982), 135–171.
    [3] L. Ali, M. Aslam, Y. A Khan, Commutativity of semirings with involution, Asian-Eur. J. Math., 13 (2020), 2050153.
    [4] Y. A. Khan, M. Aslam, L. Ali, Commutativity of additive inverse semirings through f(xy) = [x, f(y)], Thai J. Math., 2018 (2018), 288–300.
    [5] S. Sara, M. Aslam, M. Javed, On centralizer of semiprime inverse semiring, Discuss. Math. Gen. Algebra Appl., 36 (2016), 71–84. doi: 10.7151/dmgaa.1252
    [6] C. E. Rickart, Banach algebras with an adjoint operation, Ann. Math., 47 (1946), 528–550. doi: 10.2307/1969091
    [7] I. E. Segal, Irreducible representations of operator algebras, Bull. Amer. Math. Soc., 53 (1947), 73–88. doi: 10.1090/S0002-9904-1947-08742-5
    [8] K. I. Beidar, W. S. Martindale, On functional identities in prime rings with involution, J. Algebra, 203 (1998), 491–532. doi: 10.1006/jabr.1997.7285
    [9] H. E. Bell, W. S. Martindale, Centralizing mappings of semiprime rings, Can. Math. Bull., 30 (1987), 92–101. doi: 10.4153/CMB-1987-014-x
    [10] J. Berger, I. N. Herstein, J. W. Kerr, Lie ideals and derivations of prime rings, J. Algebra, 71 (1981), 259–267. doi: 10.1016/0021-8693(81)90120-4
    [11] M. Bresar, On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J., 33 (1991), 89–93. doi: 10.1017/S0017089500008077
    [12] B. E. Johnson, Continuity of derivations on commutative Banach algebras, Am. J. Math., 91 (1969), 1–10. doi: 10.2307/2373262
    [13] D. A. Jordan, On the ideals of a Lie algebra of derivations, J. London Math. Soc., 2 (1986), 33–39.
    [14] C. Lanski, Commutation with skew elements in rings with involution, Pac. J. Math., 83 (1979), 393–399. doi: 10.2140/pjm.1979.83.393
    [15] T. K Lee, On derivations of prime rings with involution, Chin. J. Math., 20 (1992), 191–203.
    [16] E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093–1100.
    [17] L. Ali, M. Aslam, Y. A. Khan, On additive maps of MA-semirings with involution, Proyecciones (Antofagasta), 39 (2020), 1097–1112. doi: 10.22199/issn.0717-6279-2020-04-0067
    [18] L. Ali, M. Aslam, Y. A. Khan, Some results on commutativity of MA-semirings, Indian J. Sci. Technol., 13 (2020), 3198–3203. doi: 10.17485/IJST/v13i31.1022
    [19] L. Ali, M. Aslam, Y. A Khan, G. Farid, On generalized derivations of semirings with involution, J. Mech. Continua Math. Sci., 15 (2020), 138–152.
    [20] I. M. Adamu, Homomorphism of intuitionistic fuzzy multigroups, Open J. Math. Sci., 4 (2020), 430–441. doi: 10.30538/oms2020.0132
    [21] P. A. Ejegwa, M. A. Ibrahim, On divisible and pure multigroups and their properties, Open J. Math. Sci., 4 (2020), 377–385. doi: 10.30538/oms2020.0127
    [22] D. A. Romano, Y. B. Jun, Weak implicative UP-filters of UP-algebras, Open J. Math. Sci., 4 (2020), 442–447. doi: 10.30538/oms2020.0133
    [23] S. Ali, A. N. A. Koam, M. A. Ansari, On*-differential identities in prime rings with involution, Hacettepe J. Math. Stat., 49 (2020), 708–715.
    [24] L. Ali, Y. A. Khan, M. Aslam, On Posner's second theorem for semirings with involution, J. Discrete Math. Sci. Cryptography, 23 (2020), 1195–1202. doi: 10.1080/09720529.2020.1809113
  • Reader Comments
  • © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(1412) PDF downloads(46) Cited by(2)

Article outline

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog