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| 摘要: |
| 本文研究了*-环R的一个core可逆元成为EP元的条件.通过对几个给定方程的解的探讨，主要证明了如下结果：设a ∈ R# ∩ R†，则a ∈ REP当且仅当下面的方程中有一个方程在χa中至少有一个解，其中χa={a，a*，a†，a#，（a#）*，（a†）*}：（1）xaa*a=a*a2x；（2）a*aa*x=xa*a*a；（3）xa*aa*=aa*a*x；（4）aa*ax=xa2a*. |
| 关键词: EP元 群可逆元 MP可逆元 方程的解 χa |
| DOI： |
| 分类号:O153.3 |
| 基金项目:国家自然科学基金资助项目 (11471282). |
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| SOME NEW CHARACTERIZATIONS ON EP ELEMENTS |
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SHI Li-yan,MA Li,WEI Jun-chao
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| Abstract: |
| In this paper, we give some conditions for a core invertible element being EP element in a *-ring R. We mainly prove the following results by discussing the solutions of some given equations: Let a ∈ R# ∩ R†. Then a ∈ REP if and only if one of the following equations has at least one solution in χa, where χa = {a, a*, a†, a#, (a#)*, (a†)*}: (1) xaa*a = a*a2x; (2) a*aa*x = xa*a*a;(3) xa*aa*= aa*a*x; (4) aa*ax = xa2a*. |
| Key words: EP element group invertible element MP invertible element the soluion of equation χa |
