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首页> 外文期刊>Journal of algebra and its applications >Characterizations for the n-strong Drazin invertibility in a ring
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Characterizations for the n-strong Drazin invertibility in a ring

机译：Characterizations for the n-strong Drazin invertibility in a ring

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Recently, a new type of generalized inverse called the n-strong Drazin inverse was introduced by Mosic in the setting of rings. Namely, let R be a ring and n be a positive integer, an element x is an element of R is called the n-strong Drazin inverse of a is an element of R if it satisfies xax = x, ax = xa and a(n) - ax is an element of Rnil. The main aim of this paper is to consider some equivalent characterizations for the n-strong Drazin invertibility in a ring. Firstly, we give an equivalent definition of the n-strong Drazin inverse, that is, x is the n-strong Drazin inverse of a if and only if xax = x, xa = ax and a - a(n+2)x is an element of Rnil. Also, we obtain some existence criteria for this inverse by means of idempotents. In particular, the n-strong Drazin invertibility of the product paq are investigated, where a is regular and p,q are arbitrary elements in a ring.

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