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- W8077602 abstract "In this chapter, we assume that V is a structured locally finite variety. It follows from the work of Parts I and II that V is the join of a strongly Abelian variety V1, an affine variety V2, and a discriminator variety V3. (See Definition 1.1 and Theorems 4.1, 5.4 and 9.6.) In this chapter, we shall prove that V is the product of these three varieties. There are several equivalent ways to formulate the result (see Theorem 0.5): (1)Every subdirect product C ≤ C1 × C2 × C3 with Ci ∈Vi (for 1 ≤ i ≤ 3) is direct, i.e., C = C1× C2 × C3.(2)Every subdirect product C ≤ C1 × C2 × C3 with Ci ∈Vi (for 1 ≤ i ≤ 3) and Ci finite is direct.(3)If C = FV(3) and Ci= FVi(3), then C ≅ C1 × C2 × C3.(4)There exists a term t(x1,x2, x3) such that t(x1, x2, 3) ≈ xi is an identity of V; (for 1 ≤ i ≤ 3); i.e., the triple of varieties (V1,V2, V3) is independent." @default.
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- W8077602 date "1989-01-01" @default.
- W8077602 modified "2023-09-23" @default.
- W8077602 title "The decomposition theorem" @default.
- W8077602 doi "https://doi.org/10.1007/978-1-4612-4552-0_14" @default.
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