| Authors | رضا جهانی نژاد,فروزان خوشایند |
|---|
| Journal | Bulletin of the Iranian Mathematical Society |
|---|
| Page number | 807 |
|---|
| Volume number | 43 |
|---|
| IF | 0.287 |
|---|
| Paper Type | Full Paper |
|---|
| Published At | 2017-06-11 |
|---|
| Journal Grade | Scientific - research |
|---|
| Journal Type | Electronic |
|---|
| Journal Country | Iran, Islamic Republic Of |
|---|
| Journal Index | ISI ,SCOPUS ,ISC |
|---|
Abstract
The aim of this paper is to generalize the notion of almost
valuation domains to arbitrary commutative rings. Also, we consider re-
lations between almost valuation rings and pseudo-almost valuation rings.
We prove that the class of almost valuation rings is properly contained
in the class of pseudo-almost valuation rings. Among the properties of
almost valuation rings, we show that a quasilocal ring R with regular max-
imal ideal M is a pseudo-almost valuation ring if and only if V = (M : M)
is an almost valuation ring with maximal ideal RadV (M). Furthermore,
we show that pseudo-almost valuation rings are precisely the pullbacks of
almost valuation rings.
