This paper studies the algorithms for coding and decoding Prufer codes of a labeled tree. The algorithms for coding and decoding Prufer codes of a labeled tree in the literatures require time usually. Although there exist linear time algorithms for Prufer-like codes [1,2,3], the algorithms utilize the integer sorting algorithms. The special range of the integers to be sorted is utilized to obta...

Invertibility of multiplication modules All rings are commutative with 1 and all modules are unital. Let R be a ring and M an R-module. M is called multiplication if for each submodule N of M, N=IM for some ideal I of R. Multiplication modules have recently received considerable attention during the last twenty years. In this talk we give the de nition of invertible submodules as a natural gene...