id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
easat-4026	Karar, Faten Ragab ; Mohammed, Fatma Elzhraa Ahmed ; Fattah, A. A. El 	The excision theory for homology theory through A_∞-algebras	2024	15	.pdf	application/pdf	7783	456	64	Definition [18] A vector space with ℤ grades is an 𝒜∞-algebras on a field 𝑀 such that: 𝒜 =⊕ 𝓅∈ℤ 𝒜𝒫, supplied with graded maps that are homogenous 𝑀-linear mappings; 𝑟𝑛:𝒜 ⊗𝑛 → 𝒜, 𝑛 ≥ 1. of (|𝑟𝑛| = 2 − 𝑛)-degree, fulfilling the subsequent requirements of Stasheff identities: ∀ 𝑛 ∈ ℕ, (𝑆𝐿(𝑛)) In the following, we describe the concept of differential graded algebras (DGAs) and how to define them using the chain complex maps and Leibniz rules.	cache/easat-4026.pdf	txt/easat-4026.txt