JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (8): 13-17.doi: 10.6040/j.issn.1671-9352.0.2022.345

Previous Articles     Next Articles

Some equivalent characterizations on EP elements

Mengge GUAN(),Hainan ZHOU,Junchao WEI*()   

  1. College of Mathematical Science, Yangzhou University, Yangzhou 225002, Jiangsu, China
  • Received:2022-06-23 Online:2023-08-20 Published:2023-07-28
  • Contact: Junchao WEI E-mail:2530374647@qq.com;jcwei@yzu.edu.cn

RichHTML

4

PDF (PC)

187

Abstract:

By studying the properties of EP elements and their association with idempotents and Jacobson radicals, some equivalent characterizations of EP elements are presented. A new structure is introduced to facilitate the equivalent characterizations of EP elements through Moore-Penrose(MP) inverses and the relationship between group inverses. Finally, by constructing some equations on the ring, the equivalent characterizations of EP elements are established by finding solutions on specific sets.

Key words: EP element, Moore-Penrose(MP) inverse, group inverse, involution ring

CLC Number: 

  • O153.3
1 KOLIHA J J , PATRICIO P . Elements of rings with equal spectral idempotents[J]. Journal of the Australian Mathematical Society, 2002, 72 (1): 137- 152.
doi: 10.1017/S1446788700003657
2 PENROSE R . A generalized inverse for matrices[J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1955, 51 (3): 406- 413.
doi: 10.1017/S0305004100030401
3 MOSIĆ D , DJORDJEVIĆ D S , KOLIHA J J . EP elements in rings[J]. Linear Algebra and its Applications, 2009, 431 (5): 527- 535.
4 DRAZIN M P . Pseudo-inverses in associative rings and semigroups[J]. The American Mathematical Monthly, 1958, 65 (7): 506- 514.
doi: 10.1080/00029890.1958.11991949
5 BEN-ISRAEL A , GREVILLE T N E . Generalized inverses: theory and applications[M]. 2nd ed New York: Springer, 2003.
6 MOSIĆ D , DJORDJEVIĆ D S . Further results on partial isometries and EP elements in rings with involution[J]. Mathematical and Computer Modelling, 2011, 54 (1/2): 460- 465.
7 DJORDJEVIĆ D S . Products of EP operators on Hilbert spaces[J]. Proceedings of the American Mathematical Society, 2001, 129 (6): 1727- 1731.
8 MOSIĆ D , DJORDJEVIĆ D S . Partial isometrics and EP elements in rings with involution[J]. The Electronic Journal of Linear Algebra, 2009, 18 (1): 761- 772.
9 YAO Hua , WEI Junchao . EP elements and *-strongly regular rings[J]. Filomat, 2018, 32 (1): 117- 125.
doi: 10.2298/FIL1801117Y
10 ZHAO Ruju , YAO Hua , WEI Junchao . EP elements and the solutions of equation in rings with involution[J]. Filomat, 2018, 32 (13): 4537- 4542.
doi: 10.2298/FIL1813537Z
11 ZHAO Ruju , YAO Hua , WEI Junchao . Characterizations of partial isometries and two special kinds of EP elements[J]. Czechoslovak Mathematical Journal, 2020, 70 (2): 539- 551.
doi: 10.21136/CMJ.2019.0389-18
12 CHEN W X . On EP elements, normal elements and partial isometries in rings with involution[J]. The Electronic Journal of Linear Algebra, 2012, 23 (1): 553- 561.
13 XU S Z , CHEN J L , BENÍTEZ J . EP elements in rings with involution[J]. Bulletin of the Malaysian Mathematical Sciences Society, 2019, 42 (6): 3409- 3426.
doi: 10.1007/s40840-019-00731-x
[1] CHENG Yang, CUI Yu-ru. Weak core inverse of core-EP decomposition [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(3): 19-24.
[2] LUO Gao-jun, ZHOU Liang, ZUO Ke-zheng. Some new characterizations of generalized and hypergeneralized projectors [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 43-48.
[3] LI Jing, HE Cheng-yuan. A fast algorithm for finding the inverse and generlized inverse of the first and the last difference circulant matrices [J]. J4, 2013, 48(6): 96-99.
[4] . The necessary and sufficient condition for the existence of limit lim λ→0 Y(λI+AY)-1 [J]. J4, 2009, 44(6): 10-13.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] Ming-Chit Liu. THE TWO GOLDBACH CONJECTURES[J]. J4, 2013, 48(2): 1 -14 .
[2] ZHAO Tong-xin1, LIU Lin-de1*, ZHANG Li1, PAN Cheng-chen2, JIA Xing-jun1. Pollinators and pollen polymorphism of  Wisteria sinensis (Sims) Sweet[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 1 -5 .
[3] WANG Kai-rong, GAO Pei-ting. Two mixed conjugate gradient methods based on DY[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 16 -23 .
[4] TANG Feng-qin1, BAI Jian-ming2. The precise large deviations for a risk model with extended negatively upper orthant dependent claim  sizes[J]. J4, 2013, 48(1): 100 -106 .
[5] CHENG Zhi1,2, SUN Cui-fang2, WANG Ning1, DU Xian-neng1. On the fibre product of Zn and its property[J]. J4, 2013, 48(2): 15 -19 .
[6] TANG Xiao-hong1, HU Wen-xiao2*, WEI Yan-feng2, JIANG Xi-long2, ZHANG Jing-ying2, SHAO Xue-dong3. Screening and biological characteristics studies of wide wine-making yeasts[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 12 -17 .
[7] ZHAO Jun1, ZHAO Jing2, FAN Ting-jun1*, YUAN Wen-peng1,3, ZHANG Zheng1, CONG Ri-shan1. Purification and anti-tumor activity examination of water-soluble asterosaponin from Asterias rollestoni Bell[J]. J4, 2013, 48(1): 30 -35 .
[8] YANG Yong-wei1, 2, HE Peng-fei2, LI Yi-jun2,3. On strict filters of BL-algebras#br#[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 63 -67 .
[9] LI Min1,2, LI Qi-qiang1. Observer-based sliding mode control of uncertain singular time-delay systems#br#[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 37 -42 .
[10] HE Hai-lun， CHEN Xiu-lan* . Circular dichroism detection of the effects of denaturants and buffers on the conformation of cold-adapted protease MCP-01 and  mesophilic protease BP01[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2013, 48(1): 23 -29 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd