Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Let K be a field, char K = 0, and let E = E(0) circle plus 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 = circle plus(g is an element of G) R((g)) is a G-graded K-algebra, then the algebra R circle times E can be G x Z(2)-graded by setting (R circle times E((g,i)) = R((g)) circle times E(i). In this article we describe the graded central polynomials for the T-prime algebras M(n)(E) congruent to M(n)(K) circle times E. As a corollary we obtain the graded central polynomials for the algebras M(a,b)(E) circle times E. As an application, we determine the Z(2)-graded identities and central polynomials for E circle times E.37620082020Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)CNPq [620025/2006-9, 302655/2005-0]FAPESP [04/13766-2, 05/60337-2]