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Title: Almost relative strongly M –flat modules

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Title:
Almost relative strongly M –flat modules
Author Name:
Dr.M.R.Aloney & Govind Sahu
Abstract:
Throughout this paper we have defined a new concept of almost strongly M-flat modules [11] and we are motivated [10]. And given several properties of them [13]. This paper concept introduced as a generalization of flat modules. There are two part in discussed In first part we study Almost strongly M-flat modules and in second section we study about the homomorphism θ_X ∶ 〖A Σ 〗_R^⨂ 〖Hom〗_(R )(X^J, N^J)→ 〖Hom〗_(A ) (〖A Σ 〗_R^⨂ X^J ,〖 AΣ 〗_(R )^⨂ N^J ) Where A is an R-algebra, X^J and N^J is R-modules. And last result we prove M be almost strongly M-flat modules then following statement are equivalent. Any finitely generated ideal I is almost M-projective Every submodule of M is almost strongly M-flat modules. Every flat module is almost strongly M-flat module.
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