Ring Regular Sequence
Given a commutative unit ring R, and an R-module M, a sequence {x_1,...,x_n} of elements of R is called a regular sequence for M (or an M-sequence for short), if, for all i=1,...,n,
1. The multiplication by x_i is injective on M/<x_1,...,x_(i-1)>M.
2. M/<x_1,...,x_n>M!=0.
If only condition (1) is fulfilled, the sequence is called weakly regular. An R-sequence is usually simply called a regular sequence.
See also
Cohen-Macaulay Ring, Regular SequenceThis entry contributed by Margherita Barile
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References
Bruns, W. and Herzog, J. Cohen-Macaulay Rings, 2nd ed. Cambridge, England: Cambridge University Press, 1998.Referenced on Wolfram|Alpha
Ring Regular SequenceCite this as:
Barile, Margherita. "Ring Regular Sequence." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/RingRegularSequence.html