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Yoneda product structure is defined on a Cartan-Eilenberg change of rings spectral sequence. Application is made to a factorization theorem for the E2-term of the Adams spectral sequence for Brown-Peterson homology of the classifying spaces BO(n). This paper gives an algebraic decomposition of the E2-term of the Adams spectral sequence of the reduced mod 2 Brown-Peterson homology [3], [4] of the classifying space BO(n). The first section gives algebraic preliminaries and the statement of the main result. In ?2 Yoneda products are introduced in a Cartan-Eilenberg change of rings spectral sequence [5] used to compute the required Ext module. The proof of the main theorem is given in ?3. The main results of ??2 and 3 are contained in the author's doctoral dissertation at the University of Chicago under Arunas Liulevicius, to whom grateful acknowledgement is made for his time and helpful suggestions. 1. Preliminaries; statement of results. This section outlines the algebraic constructions needed to construct the spectral sequence of ?2 and to introduce the main theorem. Let F be a field. An algebra A will be a positively graded, augmented, associative F-algebra. Let A denote the augmentation ideal of A. Let B*(A, A) = A @ As @ A, where As is the s-fold tensor product of A. Form the 2-sided bar construction [10] B(A, A) = Z$I>0B3(A, A) and let a denote the standard boundary map. In all that follows the degree of an element refers to its total degree. Let B(A) = F 0A B(A, A) ?A F with induced boundary a and let C(A) = B(A)* with coboundary 6 = (a)*. Recall that Z(s(A) = (A*)S and that C(A) is a differential algebra under the cup-product (1.1) [alI 'kl[ Ik1 1]1 = [1I lakiPlI I 41; Received by the editors January 10, 1975. AMS (MOS) sublect classifications (1970). Primary 55H15; Secondary 18G40. (1) The author was supported in his graduate study by a Traineeship of the National Science Foundation. 235 Copyright

Yoneda products in the Cartan-Eilenberg change of rings spectral sequence with applications to 𝐵𝑃_{∗}(𝐵𝑂(𝑛))