Sorry, no online dictionaries contain the exact phrase arithmetic semigroup.
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Reverse dictionary results:
1. abelian group
 2. algebra
3. commute
4. field
5. algebraic
6. commutative
7. derivative
8. graph
9. integral
10. inverse
 11. recursion
12. commutative group
13. commutativity
14. commutator
15. lesion
16. algebras
17. antisemigroup
18. attractor
19. attractors
20. automaton
 21. bending
22. digraph
23. functionals
24. inverse semigroup
25. manifold
26. manifolds
27. mappings
28. non-semigroup
29. semigroups
30. subspace
 31. subspaces
32. abacus
33. acalculia
34. add
35. added
36. addend
37. adder
38. adding machine
39. addition
40. adf

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