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In this paper, the definitions of algebras of quotients and Martandale-likeqoutients of Leibniz algebras are introduced and the interactions between thetwo quotients are determined. Firstly, some important properties which not onlyhold for a Leibniz algebras but also can been lifted to its algebras ofquotients are investigated. Secondly, for any semiprime Leibniz algebra, itsmaximal algebra of quotients is constucted and a Passman-like characterizationof the maximal algebra is described. Thirdly, the relationship between aLeibniz algebra and the associative algebra which is generated by left andright multiplication operators of the corresponding Leibniz algebras ofquotients are examined. Finally, the definition of dense extensions and somevital properties about Leibnia algebras via dense extensions are introduced.

Algebras of quotients and Martindale-like quotients of Leibniz algebras