Arithmetic invariants of Elliptic curves with CM defined over the field of rational numbers which have a nondegenerated ordinary reduction were investigated. A behaviour of these invariants in cyclotomic extentions was investigated. Mazur's hypothesis for the above Elliptic curves was proved. A differential field of differential invariants for action of some classical groups was described. Invariants and orbits of partial differential equations under linear trasformations of indeterminates were described. A number of papers (with U. D. Bekbaev) were devoted to the algebraic equivalence and differential algebraic invariannts of the differential equations. At present I have to deal with a structural theory of some classes nonassociative algebras as dialgebras, dendriform algebras, Leibniz algebras.

Graduated from Faculty of Mathematics and Mechanics of Leningrad State University (LSU) in 1979 (department of Higher Algebra). Ph.D. thesis was defended in 1985. A list of my works contains more than 30 titles.

1. B. A. Omirov, I. S. Rakhimov, “On Lie-like filiform Leibniz algebras”, On the classification problem of a subclass of complex filiform Leibniz algebras, Bulletin of the Australian Mathematical Society, 79 (2009), 391–404    
2. S. Albeverio, B. A.Omirov, I. S. Rakhimov, “Varieties of Nilpotent Complex Leibniz Algebras of Dimensions less then five”, On the variety of nilpotent Leibniz algebras, Communications in Algebra, 33:5 (2005), 1575–1585    
3. I. S. Rakhimov, U. D. Bekbaev, “On isomorphism classes and invariants of Finite Dimensional Complex Filiform Leibniz Algebras”, On Invariants of filiform Leibniz algebras, Communications in Algebra, 38:12 (2010), 4705–4738    

• V. I. Romanovskiy Institute of Mathematics of the Academy of Sciences of Uzbekistan, Tashkent
• National University of Uzbekistan named after M. Ulugbek, Tashkent
• Universiti Putra Malaysia