Characterizations of core and dual core inverses in rings with involution
Characterizations of core and dual core inverses in rings with involution
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DOI：
10.1080/03081087.2017.1320963
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发表时间：
2016-09
影响因子：
1.1
通讯作者：
Tingting Li;Jianlong Chen
中科院分区：
文献类型：
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作者：
Tingting Li;Jianlong Chen
设R是一个有对合的酉环。我们用厄米元（或投影）和单位给出了R中一个元素的核和对偶核逆的刻画和表示。例如，let and。那么当且仅当存在厄米元素（或投影）p使得和可逆时，a是核心可逆的。因此，当且仅当存在厄米元素（或投影）p使得且可逆时，a是一个元素。给出了正则元的核可逆性和对偶核可逆性的一个新的单位表征，并给出了它们的表达式。特别地，我们证明了当且仅当a沿a可逆时，a既是摩尔-彭罗斯可逆又是群可逆的。
ABSTRACT Let R be a unital ring with involution. We give the characterizations and representations of the core and dual core inverses of an element in R by Hermitian elements (or projections) and units. For example, let and . Then a is core invertible if and only if there exists a Hermitian element (or a projection) p such that and is invertible. As a consequence, a is an element if and only if there exists a Hermitian element (or a projection) p such that and is invertible. We also get a new characterization for both core invertibility and dual core invertibility of a regular element by units, and their expressions are shown. In particular, we prove that for , a is both Moore–Penrose invertible and group invertible if and only if is invertible along a.