Cover of the book

Graded cover









Mathematica, A problem-centered approach, 2016Second Edition
Springer Undergraduate Math. Series, Springer-Verlag, Berlin, London, New York, 2016. Amazon 

Graded rings and graded Grothendieck groups,
London Math. Society Lecture Note Series, Cambridge University Press, 2016 arXiv


Multiple commutator formulas for unitary groups, (with Nikolai Vavilov and Zuhong Zhang) arXiv
Israel Journal of Mathematics, to appear

Generation of relative commutator subgroups in Chevalley groups, (with Nikolai Vavilov and Zuhong Zhang)  arXiv
Proceedings of the Edinburgh Mathematical Society, to appear

The commutators of classical groups (with N. Vavilov, Z. Zhang), arXiv
Journal of Mathematical Sciences,, to appear

On graded irreducible representations of Leavitt path algebras, (with K. Rangaswamy), arXiv
Journal of Algebra, 450 (2016) 458–486

The yoga of commutators, further applications (with A. Stepanov, N. Vavilov, Z. Zhang),
Journal of Mathematical Sciences, 200 (2014) no. 6, 742–768.

Multiplicative groups of division rings, (with M. Mahdavi-Hezavehi, M. Motiee), arXiv
Math. Proc. Royal Irish Academy, 114 no. 1, (2014) 37-114

Leavitt path algebras are graded von Neumann regular ringsarXiv
Journal of Algebra, 401 (2014) 220–233

The graded structure of Leavitt path algebras, arXiv
Israel Journal of Mathematics, 195 (2013), 833–895

Multiple commutator formulas, (with Zuhong Zhang), arXiv
Israel Journal of Mathematics, 195 (2013), 481–505

On Quillen’s calculation of graded K-theory, (with Thomas Huettemann) arXiv
Homotopy and related structures, (2013) 8:231–238

The dynamics of Leavitt path algebras,  arXiv
Journal of Algebra, 384 (2013) 242–266

Relative commutator calculus in Chevalley groups, (with Nikolai Vavilov and Zuhong Zhang) arXiv
Journal of Algebra, 385 (2013) 262–293    

A note on the isomorphism conjectures for Leavitt path algebras,  arXiv
Journal of Algebra, 375 (2013) 33–40

Homogeneous SK_1 of simple graded algebras, (with Adrian Wadsworth), arXiv
New York Journal of Mathematics, 18 (2012) 315–336

The graded Grothendieck group and classification of Leavitt path algebras, arXiv
Math. Annalen, 355 (2013), 273–325

Stability of unitary SK_1 of Azumaya algebras,
Archiv der Math., 98 (2012), 19–23

K-theory of Azumaya algebras over schemes, (with Raymond Hoobler) arXiv
Comm. in Algebra, 41 (2013), 1268–1277

Commutator width in Chevalley groups, (with A. Stepanov, N. Vavilov, Z. Zhang)  arXiv
Note di Matematica, 33 (1) (2013), 139-170

The yoga of commutators, (with A. Stepanov, N. Vavilov, Z. Zhang), arXiv
Journal of Mathematical Sciences, 179 (2011) no. 6, 662–678

Relative unitary commutator calculus and applications, (with Nikolai Vavilov and Zuhong Zhang) arXiv
Journal of Algebra, 343 (2011) 107–137

Unitary and graded SK_1 of division algebras, (with Adrian Wadsworth) arXiv
Proc. London Math. Soc., 103 (2011) no. 3, 508–534

SK_1 of graded division algebras, (with Adrian Wadsworth) arXiv
Israel Journal of Mathematics, 183 (2011) 117–163

Generalized commutator formulas, (with Zuhong Zhang)
Comm. in Algebra, 39 (2011) 1441–1454

SK_1 of Azumaya algebras over Hensel pairs
Math. Z., 264 (2010) no. 2, 295–299. arXiv

On graded central simple algebras, (with Judith Millar)
Homotopy and related structures, 5 (2010) no. 1, 113–124 arXiv

Relative subgroups in Cheavelly groups, (with V. Petrov, N. Vavilov)
Journal of K-Theory, 5 (2010), 603–618

A note on K-theory of Azumaya algebras, (with Judith Millar)
Comm. in Algebra, 38 (2010), no. 3, 919–926

On maximal subgroups of the multiplicative group of a division algebra, (with Adrian Wadsworth)
Journal of Algebra, 322 (2009) 2528–2543 arXiv

Bak’s work on K-theory of rings, (with Nikolai Vavilov)
Journal of K-Theory, 4 (2009) 1–65
Appendix by Max Karoubi on this paper, Journal of K-Theory, 4 (2009) 67–75

Localization-completion strikes again: relative K_1 is nilpotent by abelian, (with A. Bak and N. Vavilov)
Journal of Pure Appl. Algebra, 213 (2009) 1075–1085

Nontriviality of certain quotients of K_1 groups of division algebras, (with Adrian Wadsworth)
Journal of Algebra, 312 (2007) 354–361

On the first Galois cohomology group of the algebraic group SL_1(D)
Comm. Algebra, 36:2 (2008) 381–387

Reduced K-theory for Azumaya algebras 
Journal of Algebra, 305 (2006) 687–703

A decomposition theorem for CK_1 of central simple algebras, (with Robert Wilson)
Comm. Algebra, 34 (2006) 4573–4578

Triviality of the functor Coker(K_1(F) –> K_1(D)) for division algebras, (with Uzi Vishne)
Comm. Algebra, 33 (2005) 1427–1435

K_1 of Chevalley groups are nilpotent (with Nikolai Vavilov)
Journal of Pure and Appl. Algebra, 179 (2003) 99–116

On central series of the multiplicative group of division rings 
Algebra Colloquium, 9 (2002) no. 1, 99–106

Wedderburn’s factorization theorem, Application to reduced K-theory 
Proc. American Math. Soc., 130 (2002) no. 2, 311–314

Dimension theory and nonstable K_1 of quadratic modules 
K-Theory, 27 (2002) 293–328

SK_1-like functors for division algebras 
Journal of Algebra, 239 (2001) no. 2, 573–588

Reduced K-theory and the group G(D)=D^*/F^*D’ (with M. Mahdavi-Hezavehi and B. Mirzaii)
Algebraic K-theory and its applications, H. Bass, A. Kuku, C. Pedrini (Ed.), 403–409, World Sci. Publishing, River Edge, NJ, 1999. pdf