The presented dimensions of polynomial rings. (Chinese. English summary) Zbl 1340.16005
Summary: Let \(R\) be a ring with a unit element, and \(M\) be a right \(R\)-module. The relationships between \(\text{FPd}(M_R)\) and \(\text{FPd}(M_{R[x]})\) as well as between \(\text{FPD}(R)\) and \(\text{FPD}(R[x])\) are obtained by using the presented dimensions of polynomial rings when \(R\) and \(R[x]\) are coherent rings.
MSC:
| 16E10 | Homological dimension in associative algebras |
| 16S36 | Ordinary and skew polynomial rings and semigroup rings |
| 16P70 | Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) |
