Nonsplitting sequences of value groups

Author:
Joe L. Mott

Journal:
Proc. Amer. Math. Soc. **44** (1974), 39-42

MSC:
Primary 13D99

DOI:
https://doi.org/10.1090/S0002-9939-1974-0332770-X

MathSciNet review:
0332770

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Abstract: If is the quotient field of an integral domain , then the value group of in is the group , partially ordered by , where denotes the group of units of . This note shows that if the sequence

**[1]**E. Bastida and R. Gilmer,*Overrings and divisorial ideals of rings of the form*, Michigan Math. J.**20**(1973), 79-95. MR**0323782 (48:2138)****[2]**W. Krull,*Allgermeine Bewertungstheorie*, J. Reine Angew. Math.**167**(1931), 160-196.**[3]**J. L. Mott,*The group of divisibility and its applications*, 1972 Conference on Commutative Algebra at Lawrence, Kansas, Springer-Verlag, Berlin, 1973. MR**0337943 (49:2712)****[4]**-,*Convex directed subgroups of a group of divisibility*, Canad. J. Math. (to appear). MR**0364213 (51:468)****[5]**J. Ohm,*Semi-valuations and groups of divisibility*, Canad. J. Math.**21**(1969), 576-591. MR**39**#4146. MR**0242819 (39:4146)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1974-0332770-X

Keywords:
Ordered group,
valuation,
group algebra,
lexicographically exact sequence of ordered groups,
Bezout domain

Article copyright:
© Copyright 1974
American Mathematical Society