DOI: https://doi.org/10.14710/jfma.v5i2.16363

SYARAT PERLU DAN CUKUP ELEMEN NORMAL PADA RING DENGAN ELEMEN SATUAN

*Titi Udjiani SRRM  -  Dept. of Mathematics, Universitas Diponegoro, Indonesia

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Abstract

In a ring with involution, it is possible to collect elements that are commutative with elements obtained from the results of the involution operation on itself. Such elements are called normal elements. On other hand,  rings with  involution  have elements that have Moore Penrose inverse. Elements that have  Moore Penrose inverse are not always normal. This paper discusses the necessary and sufficient conditions for elements that have  Moore Penrose inverse  is normal. The method used is  determine  set of elements that have  Moore Penrose inverse. Then take  normal elements  and determine sufficient conditions. Investigate whether the sufficient condition is a necessary condition. If yes, we obtain the necessary and sufficient condition. If not, determine else sufficient conditions for can be added to obtain the necessary and sufficient conditions.

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Keywords: Ring, Normal, Moore, Penrose.
Funding: Universitas Diponegoro under contract MetMu123456

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : ID
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  6. P. S. Reddy and K. Benebere, “Involution on Rings,” SSRN Electron. J., no. March, 2019, doi: 10.2139/ssrn.3390376
  7. O. M. Baksalary and G. Trenkler, “Characterizations of EP, normal, and Hermitian matrices,” Linear Multilinear Algebr., vol. 56, no. 3, pp. 299–304, 2008, doi: 10.1080/03081080600872616
  8. W. Chen, “On EP elements, normal elements and partial isometries in rings with involution,” Electron. J. Linear Algebr., vol. 23, no. 174007, pp. 553–561, 2012, doi: 10.13001/1081-3810.1540
  9. D. S. Djordjević, “Characterizations of normal, hyponormal and EP operators,” J. Math. Anal. Appl., vol. 329, no. 2, pp. 1181–1190, 2007, doi: 10.1016/j.jmaa.2006.07.008
  10. D. Mosić and D. S. Djordjević, “Moore-Penrose-invertible normal and Hermitian elements in rings,” Linear Algebra Appl., vol. 431, no. 5–7, pp. 732–745, 2009, doi: 10.1016/j.laa.2009.03.023
  11. Y. Qu, J. Wei, and H. Yao, “Characterizations of normal elements in rings with involution,” Acta Math. Hungarica, vol. 156, no. 2, pp. 459–464, 2018, doi: 10.1007/s10474-018-0874-z
  12. A. Ben-Israel, “The Moore of the Moore-Penrose inverse,” Electron. J. Linear Algebr., vol. 9, no. August, pp. 150–157, 2002, doi: 10.13001/1081-3810.1083
  13. E. Boasso, “Moore-Penrose inverse and doubly commuting elements in $C^*$-algebras,” pp. 35–44, 2013, [Online]. Available: http://arxiv.org/abs/1309.6911
  14. D. Mosić and D. S. Djordjević, “Weighted partial isometries and weighted-EP elements in C∗-algebras,” Appl. Math. Comput., vol. 265, no. 174007, pp. 17–30, 2015, doi: 10.1016/j.amc.2015.04.102
  15. D. Mosić, C. Deng, and H. Ma, “On a weighted core inverse in a ring with involution,” Commun. Algebr., vol. 46, no. 6, pp. 2332–2345, 2018, doi: 10.1080/00927872.2017.1378895
  16. T. Udjiani and Suryoto, “Commutative symmetric element in a ring with involution,” J. Phys. Conf. Ser., vol. 1943, no. 1, pp. 1–4, 2021, doi: 10.1088/1742-6596/1943/1/012116

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