Semigroup graded algebras and graded PI-exponent
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E. Aljadeff and A. Giambruno, Multialternating graded polynomials and growth of polynomial identities, Proceedings of the American Mathematical Society 141 (2013), 3055–3065.
E. Aljadeff, A. Giambruno and D. La Mattina, Graded polynomial identities and exponential growth, Journa; für die Reine und Angewandte Mathematik 650 (2011), 83–100.
Y. A. Bahturin, Identical Relations in Lie Algebras, VNU Science Press, Utrecht, 1987.
Y. A. Bahturin and M. V. Zaicev, Graded algebras and graded identities, Polynomial identities and combinatorial methods, in Polynomial Identities and Combinatorial Methods (Pantelleria, 2001), Lecture Notes in Pure and Applied Mathematics, Vol. 235, Dekker, New York, 2003, pp. 101–139.
Y. A. Bahturin and M. V. Zaicev, Group gradings on matrix algebras, Canadian Mathematical Bulletin 45 (2002), 499–508
Y. A. Bahturin and M. V. Zaicev, Semigroup gradings on associative rings, Advances in Applied Mathematics 37 (2006), 153–161.
Y. A. Bakhturin, M. V. Zaicev and S. K. Sehgal, Finite-dimensional simple graded algebras, Matematicheskiĭ Sbornik 199 (2008), 21–40; translation in Sbornik. Mathematics 199 (2008), 965–983.
O. A. Bogdanchuk, S. P. Mishchenko and A. B. Verëvkin, On Lie algebras with exponential growth of codimensions, Serdica Mathematical Journal 40 (2014), 209–240.
M. V. Clase, Semigroup graded rings, Ph.D. Thesis, Memorial University of Newfoundland, Canada, 1993.
M. V. Clase and E. Jespers, On the Jacobson radical of semigroup graded rings, Journal of Algebra 169 (1994), 79–97.
A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups. Vol. I, Mathematical Surveys, Vol. 7, American Mathematical Society, Providence, RI, 1961.
V. S. Drensky, Free Algebras and PI-algebras: Graduate Course in Algebra, Springer-Verlag, Singapore, 2000.
A. Giambruno and D. La Mattina, Graded polynomial identities and codimensions: computing the exponential growth, Advances in Mathematics 225 (2010), 859–881.
A. Giambruno, S. Mishchenko and M. Zaicev, Codimensions of algebras and growth functions, Advances in Mathematics 217 (2008), 1027–1052.
A. Giambruno and M. Zaicev, On codimension growth of finitely generated associative algebras, Advances in Mathematics 140 (1998), 145–155.
A. Giambruno and M. Zaicev, Exponential codimension growth of PI algebras: an exact estimate, Advances in Mathematics 142 (1999), 221–243.
A. Giambruno and M. V. Zaicev, Polynomial Identities and Asymptotic Methods, Mathematical Surveys and Monographs, Vol. 122, American Mathematical Society, Providence, RI, 2005.
A. S. Gordienko, Amitsur’s conjecture for associative algebras with a generalized Hopf action, Journal of Pure and Applied Algebra 217 (2013), 1395–1411.
A. S. Gordienko, Asymptotics of H-identities for associative algebras with an H-invariant radical, Journal of Algebra 393 (2013), 92–101.
A. S. Gordienko, Amitsur’s conjecture for polynomial H-identities of H-module Lie algebras, Transactions of the American Mathematical Society 367 (2015), 313–354.
A. S. Gordienko, Semigroup graded algebras and codimension growth of graded polynomial identities, Journal of Algebra 438 (2015), 235–259.
A.S. Gordienko, Co-stability of radicals and its applications to PI-theory, Algebra Colloqium 23 (2016), 481–492.
I. N. Herstein, Noncommutative Rings, The Carus Mathematical Monographs, Vol. 15, John Wiley and sons, New York, 1968.
A.V. Kelarev, Ring Constructions and Applications, Series in Algebra, Vol. 9, World Scientific Publishing, River Edge, NJ, 2002.
S. P. Mishchenko and M. V. Zaicev, An example of a variety of Lie algebras with a fractional exponent, Journal of Mathematical Sciences (New York) 93 (1999), 977–982.
S. P. Mishchenko, A. B. Verevkin and M. V. Zaicev, A sufficient condition for coincidence of lower and upper exponents of the variety of linear algebras, Moscow University Mathematics Bulletin 66 (2011), 86–89.
J. Okninski, Semigroup Algebras, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 138, Marcel Dekker, New York, 1991.
P. Wauters and E. Jespers, Rings graded by an inverse semigroup with finitely many idempotents, Houston Journal of Mathematics 15 (1989), 291–304.