Abstract：This paper aims to investigate the composition of(Manis) valuations on a(commutative) ring.For a valuation v on a commutative ring R and an isolated subgroup Δ of the value group of v,the so-called first and second valuations induced by v with Δ were defined,where Δ is an isolated subgroup of the value group of v.Several results were obtained on the induced valuations.Another important result was that for a valuation v on a ring R and a valuation w with null core on the residue ring of v,it existed a unique valuation v on R such that the first and second valuations induced by v with Δ were equivalent to u and w,respectively.The reality of this composed valuation v was also investigated,and a necessary and sufficient condition for v to be a real valuation was obtained.
2012, Vol. 36 
