Let K be a field, char K = 0, and let E = E 0 ⊕ E 1 be the Grassmann algebra of infinite dimension over K, equipped with its natural ℤ 2-grading. If G is a finite abelian group and R = ⊕ g∈GR (g) is a G-graded K-algebra, then the algebra R ⊗ E can be G × ℤ 22-graded by setting (R ⊗ E) (g,i) = R (g) ⊗ E i. In this article we describe the graded central polynomials for the T-prime algebras M n(E) ≅ M n(K) ⊗ E. As a corollary we obtain the graded central polynomials for the algebras M a,b(E) ⊗ E. As an application, we determine the ℤ 2-graded identities and central polynomials for E ⊗ E. © Taylor & Francis Group, LLC.37620082020Kemer, A., (1991) Ideals of Identities of Associative Algebras, , Translations Math. Monographs 87. Providence, RI: Amer. Math. SocVasilovsky, S.Y., ℤ n-graded polynomial identities of the full matrix algebra of order n (1999) Proc. Amer. Math. Soc., 127 (12), pp. 3517-3524Azevedo, S.S., Graded identities for the matrix algebra of order n over an infinite field (2002) Commun. Algebra, 30 (12), pp. 5849-5860Krakowski, D., Regev, A., The polynomial identities of the Grassmann algebra (1973) Trans. A.M.S., 181, pp. 429-438Popov, A., Identities of the tensor square of a Grassmann algebra (1982) Algebra Logic, 21, pp. 296-316Di Vincenzo, O.M., Nardozza, V., Graded polynomial identities for tensor products by the Grassmann algebra (2003) Commun. Alg., 31 (3), pp. 1453-1474Azevedo, S.S., Fidellis, M., Koshlukov, P., Graded identities and PI equivalence of algebras in positive characteristic (2005) Commun. Algebra, 33 (4), pp. 1011-1022Formanek, E., Central polynomials for matrix rings (1972) J. Algebra, 23, pp. 129-132Razmyslov Yu., P., On a problem of Kaplansky (1973) Math. USSR, Izv., 7, pp. 479-496Okhitin, S., Central polynomials of the algebra of second order matrices (1988) Moscow Univ. Math. Bull., 43 (4), pp. 49-51Colombo, J., Koshlukov, P., Central polynomials in the matrix algebra of order two (2004) Linear Algebra Appl., 377, pp. 53-67Brandão, A., Koshlukov, P., Krasilnikov, A., (2007) Graded Central Polynomials for the Matrix Algebra of Order Two, , To appear Monatshefte für Mathematik, 2009Brandão, A., Koshlukov, P., Central polynomials for2-graded algebras and for algebras with involution (2007) J. Pure Appl. Algebra, 208, pp. 877-886Di Vincenzo, O.M., Cocharacters of G-graded algebras (1996) Commun. Algebra, 24 (10), pp. 3293-3310Kemer, A., Varieties and ℤ2-graded algebras (1985) Math. USSR Izv., 25, pp. 359-374Brandao, A., Graded Central Polynomials for the Algebra M n K (2007) Rendiconti del Circolo Mathematico di Palermo, 57 (2), pp. 265-278Alves, S.M., Koshlukov, P., Polynomial identities of algebras in positive characteristic (2006) J. Algebra, 305 (2), pp. 1149-1165Di Vincenzo, O.M., On the graded identities of M 1,1 (1992) E. Israel J. Math., 80 (3), pp. 323-335Koshlukov, P., Azevedo, S.S., Graded identities for T-prime algebras over fields of positive characteristic (2002) Israel J. Math., 128, pp. 157-176Razmyslov Yu., P., Finite basing of the identities of a matrix algebra of second order over a field of characteristic zero (1973) Algebra Logic, 10, pp. 47-63Drensky, V., A minimal basis for the identities of a second-order matrix algebra over a field of characteristic 0 (1980) Algebra Logic, 20, pp. 188-194