Pure ideals in commutative reduced Gelfand rings with unity
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In this paper, pure ideals in the class of all commutative reduced Gelfand rings with unity are classified. Then as an application, we prove that any pure ideal in the ring C(X) of all continuous real valued functions over a completely regular Hausdorff space has the form \(\cap_{x\in K}0_ x \), where K is a closed subset of the Stone- Čech compactification \(\beta\) X of X.
- University of Jordan Jordan
Structure, classification theorems for modules and ideals in commutative rings, pure ideal, reduced Gelfand rings, Algebraic properties of function spaces in general topology, Ideals and multiplicative ideal theory in commutative rings, ring of continuous real valued functions
Structure, classification theorems for modules and ideals in commutative rings, pure ideal, reduced Gelfand rings, Algebraic properties of function spaces in general topology, Ideals and multiplicative ideal theory in commutative rings, ring of continuous real valued functions
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