In the following paper (Example 2.1), it has been mentioned to K+M to provide an example of a pseudo valuation domain which is not a valuation ring, and its reference is Gilmer's book, but I have no access to Gilmer's book.
Can someone help me and explain what K+M is?
Hedstrom, J. R.; Houston, E. G., Pseudo-valuation domains. II, Houston J. Math. 4, 199-207 (1978). ZBL0416.13014.
A "valuation ring of the form $K+M$" is a valuation ring $V$ with maximal ideal $M$ such that $V$ contains a subring $K$ which is a field and one has $V=K+M:=\{k+m\,|\,k\in K,m\in M\}$.
In this case (see the paper), for every proper subfield $F$ of $K$, the set $F+M:=\{f+m\,|\,f\in F,m\in M\}$ --- call it $R$ --- is a subring of $V$ which is a pseudo-valuation ring but not a valuation ring.
