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초록· 키워드
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If m and n are non-negative integers, then three new classesof abelian p-groups are defined and studied: the m, n-simply presentedgroups, the m, n-balanced projective groups and the m, n-totally projec-tive groups. These notions combine and generalize both the theories ofsimply presented groups and pw+n-projective groups. If m, n = 0, theseall agree with the class of totally projective groups, but when m+n≥1,they also include the pw+m+n-projective groups. These classes are relatedto the (strongly) n-simply presented and (strongly) n-balanced projectivegroups considered in [15] and the n-summable groups considered in [2].
The groups in these classes whose lengths are less than w2 are characterized, and if in addition we have n = 0, they are determined by isometriesof their pm-socles.
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참고문헌 (20)
참고문헌 신청
C. Megibben / 1969 / The generalized Kulikov criterion / Canad. J. Math 21 : 1192 ~ 1205
D. Cutler / 1970 / Another summable CΩ-group / Proc. Amer. Math. Soc 26 : 43 ~ 44
F. Richman / 1979 / Valuated groups / J. Algebra 56 (1) : 145 ~ 167
J. Irwin / 1993 / Primary abelian groups and direct sums of cyclics / J. Algebra 159 (2) : 387 ~ 399
K. Honda / 1964 / Realism in the theory of abelian groups III / Comment. Math. Univ. St. Pauli 12 : 75 ~ 111
D. Cutler / 1970 / Another summable CΩ-group / Proc. Amer. Math. Soc 26 : 43 ~ 44
F. Richman / 1979 / Valuated groups / J. Algebra 56 (1) : 145 ~ 167
J. Irwin / 1993 / Primary abelian groups and direct sums of cyclics / J. Algebra 159 (2) : 387 ~ 399
K. Honda / 1964 / Realism in the theory of abelian groups III / Comment. Math. Univ. St. Pauli 12 : 75 ~ 111
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