Normality and Related Properties of Forcing Algebras

The authors present a sufficient condition for irreducibility of forcing algebras and study the (non)reducedness phenomenon. Furthermore, the authors prove a criterion for normality of forcing algebras over a polynomial base ring with coefficients in a perfect field. This gives over algebraically closed fields a geometrical normality criterion for algebraic (forcing) varieties. Besides, the authors examine in detail a specific (enlightening) example with several forcing equations. Finally, the authors compute explicitly the normalization of a particular forcing algebra by means of finding explicitly the generators of the ideal defining it as an affine ring.