In the paper we prove that there exists a simultaneous reduction of one-parameter family of $\mathfrak{m}_{n}$-primary ideals in the ring of germs of holomorphic functions. Moreover, we generalize the result of A. Płoski [8] on the semicontinuity of the Łojasiewicz exponent in a multiplicity-constant deformation.
Kodai Math. J.
38(1):
201-208
(March 2015).
DOI: 10.2996/kmj/1426684450
