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Abstract
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.
ACKNOWLEDGMENT
Danny de Jesús Gómez-Ramírez would like to thank to his parents José Omar Gómez Torres and Luz Stella Ramírez Correa for all the assistance, love, and inspiration. Besides, he wishes to thank the German Academic Exchange Service (DAAD) for the financial and academic support.