sentences:  Catenary ring
  
  In mathematics, a commutative ring "R" is catenary if for any pair of prime ideals 
  
  any two strictly increasing chains 
  
  are contained in maximal strictly increasing chains from "p" to "q" of the same (finite) length.In a geometric situation, in which the dimension of an algebraic variety attached to a prime ideal will decrease as the prime ideal becomes bigger, the length of such a chain "n" is usually the difference in dimensions.