Some properties of smooth ideals (Q1396243)

The authors introduce the notion of a smooth ideal base, i.e., a nonzero function \({\mathcal B}:I^X\rightarrow I\) satisfying the following conditions: (1) \({\mathcal B}(\tilde{1})=0\); (2) \({\mathcal B}(\lambda\vee \mu)\geq {\mathcal B}(\lambda)\wedge {\mathcal B}(\mu)\), for \(\lambda,\mu\in I^X\). They investigate the images and preimages of smooth ideals and ideal bases and define the product of smooth ideals.