By Robert B. Warfield Jr. (auth.), David M. Arnold, Roger H. Hunter, Elbert A. Walker (eds.)
Read or Download Abelian Group Theory: Proceedings of the 2nd New Mexico State University Conference, Held at Las Cruces, New Mexico, December 9–12, 1976 PDF
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Additional info for Abelian Group Theory: Proceedings of the 2nd New Mexico State University Conference, Held at Las Cruces, New Mexico, December 9–12, 1976
2 (1965), 432-442. ii. P. Crawley and A. W. Hales, The structure of Abelian p-groups by certain presentations, J. AIg. 12 (1969), 10-23. 12. E. G. , Krull-Schmidt and cancellation Pacific J. , 46 (1973), 115-121. in direct given over local rings, 36 13. L. Fuchs, Notes on Abelian groups, II, Acta Math. Acad. Sci. Hungar. Ii~(1960), 117-125. 14. L. , 75 (1971), 198-204. 15. L. Fuchs, Infinite Abelian Groups. vol. II, Academic Press, New York, 1973. 16. K. ~R. Goodearl, Power cancellation of groups and modules, Pacific J.
Suppose x I e (M;p) (A). Let v = M . p zero integers and a i ~ ( v * A ~ M ( A ) ) U M * ( A ) , Write x I = Zriai, where r. are nonx the generating set of (M;p)*(A). Since X is a decomposition basis, there is an integer s such that sria i is in [X] for all i. If we write sria i = ZjcitijY j, then sy I = ZieitilY I. Then there is at least one non-zero til for which the p-factor of s is equal to the p-factor of til. For this i, we have Hp(Sy I) ~ H p ( s r i a i) ~ ( t i l Y so a i ~ v*A~M(A). I) = Hp(SYl), But H(sy I) ~ H(sria i) ~ H(tilYl), implies H(ai) is compatible with M.
Yen, Modules over a complete discrete valuation ring, Trans. Amer. Math. Soc. 98(1961), 242-254. 18. O. Stanton, An invariant for modules over a discrete valuation ring, Proc. Amer. Math. Soc. 49(1975), 51-54. 19. H. Ulm, Zur Theorie der abzahlbar-unendlichen abelschen Gruppen, Math. , 107(1933), 774-803. 20. A. Walker, Ulm's theorem for totally projective groups, Proc. Amer. Math. Soc. 37(1973), 387-392. 21. D.
Abelian Group Theory: Proceedings of the 2nd New Mexico State University Conference, Held at Las Cruces, New Mexico, December 9–12, 1976 by Robert B. Warfield Jr. (auth.), David M. Arnold, Roger H. Hunter, Elbert A. Walker (eds.)