交换环上M-赋值的分解

Decomposition of M-Valuations on a Commutative Ring

研究交换环上M-赋值的分解与合成。通过在序幺半群上引进融洽同余,交换环上M-赋值被分解为一个可消M-赋值及其剩余环的一个核为零的Manis赋值。反之,对于交换环上一个可消M-赋值及其剩余环的一个核为零的Manis赋值,该环的一个M-赋值被合成,使得它能通过所述的分解回复到两个给定的赋值。

The purpose of this paper is to investigate the decomposition and composition of M - valuations on a commutative ring. By introducing the notion of harmonic congruences for ordered monoids, a M - valuation on a commuttative ring is decomposed into a cancellative M- valuation and a Manis valuation with null core on the residue ring of this cancellative M - valuation. Conversely, for a cancellative M - valuation and a Manis valuation with null core on the residue ring of this cancellatiue M - valuation, a M - valuation is so composed that it can be turned back into the given valuations by such a decomposition.