Von Neumann Regular ${\mathcal{C}}^{\infty }-$Rings and Applications

Abstract

In this paper we present the notion of a von Neumann regular ${\mathcal{C}}^{\infty }-$ring, we prove some results about them and we describe some of their properties. We prove, using two different methods, that the category of von Neumann regular ${\mathcal{C}}^{\infty }-$rings is a reflective subcategory of ${\mathcal{C}}^{\infty }\mathbf{Rng}$. We prove that every homomorphism between Boolean algebras can be represented by a ${\mathcal{C}}^{\infty }-$ring homomorphism between von Neumann regular ${\mathcal{C}}^{\infty }-$rings.

72 pages

References in corpus (1)

• A Universal Algebraic Survey of ${\mathcal{C}}^{\infty }-$Rings

Cited by in corpus (1)

• Separation Theorems in Smooth Commutative Algebra and Applications