... B and C are ideals of an algebra A, and that as avector space A is the direct sum of B and C (A = B + C, B ∩ C = 0).Then A is called the direct sum A = B ⊕ C of B and C as algebras.The vector ... includedwith this eBook or online at www.gutenberg.orgTitle: An Introduction to Nonassociative AlgebrasAuthor: R. D. SchaferRelease Date: April 24, 2008 [EBook #25156]Language: English Character ... is an algebra over F , the sets Bof all pairs (b, 0) with b in Band Cof all pairs (0, c) with c in C are ideals of A isomorphic respec-tively to B and C, and A = B⊕ C. By the customary...