Open the door to the atomic world by single-molecule atomic force microscopy
- Award ID(s):
- 1661699
- PAR ID:
- 10294049
- Date Published:
- Journal Name:
- Matter
- Volume:
- 4
- Issue:
- 4
- ISSN:
- 2590-2385
- Page Range / eLocation ID:
- 1189 to 1223
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract LetMbe a cancellative and commutative (additive) monoid. The monoidMis atomic if every non-invertible element can be written as a sum of irreducible elements, which are also called atoms. Also,Msatisfies the ascending chain condition on principal ideals (ACCP) if every increasing sequence of principal ideals (under inclusion) becomes constant from one point on. In the first part of this paper, we characterize torsion-free monoids that satisfy the ACCP as those torsion-free monoids whose submonoids are all atomic. A submonoid of the nonnegative cone of a totally ordered abelian group is often called a positive monoid. Every positive monoid is clearly torsion-free. In the second part of this paper, we study the atomic structure of certain classes of positive monoids.more » « less
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