Additively irreducible sequences in commutative semigroups

作者：Wang, Guoqing^*

来源：Journal of Combinatorial Theory - Series A, 2017, 152: 380-397.

DOI：10.1016/j.jcta.2017.07.001

• Irreducible sequences
• The Davenport constant
• Noetherian semigroups
• Finite principal ideal rings
• Schiitzenberger groups

Let S be a commutative semigroup, and let T be a sequence of terms from the semigroup S. We call T an (additively) irreducible sequence provided that no sum of some of its terms vanishes. Given any element a of S, let D-a (S) be the largest length of an irreducible sequence such that the sum of all terms from the sequence is equal to a. In the case that any ascending chain of principal ideals starting from the ideal (a) terminates in S, we find necessary and sufficient conditions for D-a (S) to be finite, and in particular, we give sharp lower and upper bounds for D-a (S) in case D-a (S) is finite. We also apply the result to commutative unitary rings. As a special case, the value of D. (8) is determined when S is the multiplicative semigroup of any finite commutative principal ideal unitary ring.

• 出版日期2017-11
• 单位天津工业大学