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Communications in Algebra Volume 29, 2001 - Issue 9
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Original Articles

POLYNOMIAL IDENTITIES ON SUPERALGEBRAS AND ALMOST POLYNOMIAL GROWTH

A. Giambruno Dipartimento di Matematica ed Applicazioni, Università di Palermo, Palermo, 90123, Italy
,
S. Mishchenko Department of Algebra and Geometric Computations, Faculty of Mathematics and Mechanics, Ulyanovsk State University, Ulyanovsk, 432700, Russia
&
M. Zaicev Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899, Russia
Pages 3787-3800 | Received 01 Feb 2001, Published online: 01 Feb 2007

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D. C. L. Bessades, R. B. dos Santos, M. L. O. Santos & A. C. Vieira. (2021) Superalgebras and algebras with involution: classifying varieties of quadratic growth. Communications in Algebra 49:6, pages 2476-2490.
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T. S. do Nascimento & A. C. Vieira. (2019) Superalgebras with graded involution and star-graded colength bounded by 3. Linear and Multilinear Algebra 67:10, pages 1999-2020.
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Antonio Giambruno, Rafael Bezerra dos Santos & Ana Cristina Vieira. (2016) Identities of *-superalgebras and almost polynomial growth. Linear and Multilinear Algebra 64:3, pages 484-501.
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Sandra Mara Alves Jorge. (2010) On Graded Central Polynomials of the Graded Algebra M 2(E). Communications in Algebra 38:6, pages 2184-2198.
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Viviane Ribeiro Tomaz da Silva. (2009) ℤ2-Codimensions of the Grassmann Algebra. Communications in Algebra 37:9, pages 3342-3359.
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Onofrio Mario Di Vincenzo & Vincenzo Nardozza. (2003) Graded Polynomial Identities for Tensor Products by the Grassmann Algebra. Communications in Algebra 31:3, pages 1453-1474.
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Carla Rizzo. (2023) Differential codimensions and exponential growth. Linear Algebra and its Applications 675, pages 294-311.
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Carla Rizzo, Rafael Bezerra dos Santos & Ana Cristina Vieira. (2022) Differential Identities and Polynomial Growth of the Codimensions. Algebras and Representation Theory 26:5, pages 2001-2014.
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L. M. C. Oliveira, R. B. dos Santos & A. C. Vieira. (2021) Varieties of Group Graded Algebras with Graded Involution of Almost Polynomial Growth. Algebras and Representation Theory 26:3, pages 663-677.
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Fabrizio Martino & Carla Rizzo. (2022) Differential identities and varieties of almost polynomial growth. Israel Journal of Mathematics 254:1, pages 243-274.
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W.D.S. Costa, A. Ioppolo, R.B. dos Santos & A.C. Vieira. (2021) Unitary superalgebras with graded involution or superinvolution of polynomial growth. Journal of Pure and Applied Algebra 225:9, pages 106666.
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Antonio Ioppolo, Plamen Koshlukov & Daniela La Mattina. (2021) Trace identities and almost polynomial growth. Journal of Pure and Applied Algebra 225:2, pages 106501.
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Antonio Ioppolo, Plamen Koshlukov & Daniela La Mattina. 2021. Polynomial Identities in Algebras. Polynomial Identities in Algebras 211 225 .
Tatiana Aparecida Gouveia, Rafael Bezerra dos Santos & Ana Cristina Vieira. (2020) Minimal ⁎-varieties and minimal supervarieties of polynomial growth. Journal of Algebra 552, pages 107-133.
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Fabrizio Martino. (2019) Varieties of special Jordan algebras of almost polynomial growth. Journal of Algebra 531, pages 184-196.
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Antonio Giambruno, Antonio Ioppolo & Daniela La Mattina. (2018) Superalgebras with Involution or Superinvolution and Almost Polynomial Growth of the Codimensions. Algebras and Representation Theory 22:4, pages 961-976.
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Luís Felipe Gonçalves Fonseca. (2018) ℤ2-graded identities of the Grassmann algebra over a finite field. International Journal of Algebra and Computation 28:02, pages 291-307.
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Antonio Ioppolo & Daniela La Mattina. (2017) Polynomial codimension growth of algebras with involutions and superinvolutions. Journal of Algebra 472, pages 519-545.
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Onofrio Mario Di Vincenzo & Ernesto Spinelli. (2015) Minimal varieties of associative PI (super)-algebras with respect to their (graded) exponent. São Paulo Journal of Mathematical Sciences 10:2, pages 248-262.
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Lucio Centrone. (2016) The $G$-graded identities of the Grassmann Algebra. Archivum Mathematicum:3, pages 141-158.
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Plamen Koshlukov & Daniela La Mattina. (2015) Graded algebras with polynomial growth of their codimensions. Journal of Algebra 434, pages 115-137.
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T.S. do Nascimento, R.B. dos Santos & A.C. Vieira. (2015) Graded cocharacters of minimal subvarieties of supervarieties of almost polynomial growth. Journal of Pure and Applied Algebra 219:4, pages 913-929.
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Daniela La Mattina. (2015) Almost polynomial growth: Classifying varieties of graded algebras. Israel Journal of Mathematics 207:1, pages 53-75.
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Onofrio M. Di Vincenzo & Viviane Ribeiro Tomaz da Silva. (2014) On -graded identities of the generalized Grassmann envelope of the upper triangular matrices. Journal of Pure and Applied Algebra 218:2, pages 285-296.
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A.C. Vieira. (2013) Supervarieties of small graded colength. Journal of Pure and Applied Algebra 217:2, pages 322-333.
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Onofrio Mario Di Vincenzo & Ernesto Spinelli. (2012) On some minimal supervarieties of exponential growth. Journal of Algebra 368, pages 182-198.
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Viviane Ribeiro Tomaz da Silva. (2011) On ℤ2-graded identities of the super tensor product of UT 2(F) by the Grassmann algebra. Israel Journal of Mathematics 188:1, pages 441-462.
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Lucio Centrone. (2011) -graded identities of the Grassmann algebra in positive characteristic . Linear Algebra and its Applications 435:12, pages 3297-3313.
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Daniela La Mattina. (2011) Varieties of superalgebras of almost polynomial growth. Journal of Algebra 336:1, pages 209-226.
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Angela Valenti. (2011) Group graded algebras and almost polynomial growth. Journal of Algebra 334:1, pages 247-254.
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Onofrio M. Di Vincenzo & Vincenzo Nardozza. (2010) On a Regev-Seeman conjecture about ℤ2-graded tensor products. Israel Journal of Mathematics 176:1, pages 43-59.
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D. La Mattina, S. Mauceri & P. Misso. (2009) Polynomial growth and identities of superalgebras and star-algebras. Journal of Pure and Applied Algebra 213:11, pages 2087-2094.
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Onofrio M. Di Vincenzo & Viviane Ribeiro Tomaz da Silva. (2009) On -graded polynomial identities of the Grassmann algebra . Linear Algebra and its Applications 431:1-2, pages 56-72.
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A. Giambruno & S. Mishchenko. (2008) Super-cocharacters, star-cocharacters and multiplicities bounded by one. manuscripta mathematica 128:4, pages 483-504.
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A. Giambruno, D. La Mattina & P. Misso. (2006) Polynomial identities on superalgebras: Classifying linear growth. Journal of Pure and Applied Algebra 207:1, pages 215-240.
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A. Giambruno, S. Mishchenko & M. Zaicev. (2006) Algebras with intermediate growth of the codimensions. Advances in Applied Mathematics 37:3, pages 360-377.
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S. Mishchenko & A. Valenti. (2005) A Leibniz variety with almost polynomial growth. Journal of Pure and Applied Algebra 202:1-3, pages 82-101.
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Francesca Benanti, Antonio Giambruno & Manuela Pipitone. (2003) Polynomial identities on superalgebras and exponential growth. Journal of Algebra 269:2, pages 422-438.
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Onofrio Mario Di Vincenzo. 2003. Polynomial Identities And Combinatorial Methods. Polynomial Identities And Combinatorial Methods.
Angela Valenti. 2003. Polynomial Identities And Combinatorial Methods. Polynomial Identities And Combinatorial Methods.
Antonio Giambruno. 2003. Polynomial Identities And Combinatorial Methods. Polynomial Identities And Combinatorial Methods.

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