Let R be a unital*-ring.For any a,w,b ∈ R,we apply the w-core inverse to define a new class of partial orders in R,called the w-core partial order.Suppose that a,b ∈ R are w-core invertible.We say that a is below b under the w-core partial order if a(#)w a=a(#)w b and awa(#)w=bwa(#)w,where a(#)w denotes the w-core inverse of a.Characterizations of the w-core partial order are given,and its relationships with several types of partial orders are also considered.In particular,we show that the core partial order coincides with the a-core partial order,and the star partial order coincides with the a*-core partial order.
w-core inverseinverse along an elementsharp partial orderstar partial ordercore partial orderrings with involution
Huihui Zhu、Liyun Wu
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School of Mathematics Hefei University of Technology,Hefei 230009,China
National Natural Science Foundation of ChinaChina Postdoctoral Science Foundation
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