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- Publisher
- Springer Journals
- Copyright
- Copyright © 2016 by Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia
- Subject
- Mathematics; Mathematics, general; Applications of Mathematics
- ISSN
- 0126-6705
- eISSN
- 2180-4206
- DOI
- 10.1007/s40840-016-0318-2
- Publisher site
- See Article on Publisher Site
Abstract
We study the Drazin inverses of the sum and the product of two elements in a ring. Given two Drazin invertible elements a and b such that $$a^2b=aba$$ a 2 b = a b a and $$b^2a=bab$$ b 2 a = b a b , it is shown that ab is Drazin invertible and that $$a+b$$ a + b is Drazin invertible if and only if $$1+a^Db$$ 1 + a D b is Drazin invertible. Moreover, the formulae of $$(ab)^D, (a+b)^D$$ ( a b ) D , ( a + b ) D and $$(1+a^Db)^D$$ ( 1 + a D b ) D are presented.
Journal
Bulletin of the Malaysian Mathematical Sciences Society – Springer Journals
Published: Feb 20, 2016