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Decompositions of commutative monoid congruences and binomial ideals
Decompositions of commutative monoid congruences binomial ideals Commutative Algebra
2011/9/19
Abstract: We demonstrate how primary decomposition of commutative monoid congruences fails to capture the essence of primary decomposition in commutative rings by exhibiting a more sensitive theory of...
Proofs of power sum and binomial coefficient congruences via Pascal's identity
binomial coefficient Pascal's identity
2010/11/8
A frequently cited theorem says that for n > 0 and prime p, the sum of the first p n-th powers is congruent to -1 modulo p if p-1 divides n, and to 0 otherwise. We survey the main ingredients in seve...
Some new super-congruences modulo prime powers
super-congruences modulo prime powers math
2010/11/22
Let $p>3$ be a prime. We show that $$\sum_{k=0}^{p-1}\binom(-1/(p+1),k)^{p+1}=0 (mod p^5).$$ For any positive integer m not divisible by p, we prove that $$\sum_{k=0}^{p-1}(-1)^{km}\binom(p/m-1,k)^m=0...