On induced modules over locally Abelian-by-polycyclic groups of finite rank
DOI:
https://doi.org/10.15407/dopovidi2019.06.008Keywords:
group rings, induced modules, particle rings, primitive algebrasAbstract
We develop some methods for studying the modules over group rings, which are based on properties of induced modules and on the embedding of these modules in the modules over rings of quotients of group rings. Using these methods, we have obtained the criteria of primitivity for group algebras of certain classes of locally soluble groups.
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Tushev, A. V. (2000). On primitive representations of soluble groups of finite rank. Sb. Mat., 191, No. 11, pp. 1707-1748. doi: https://doi.org/10.1070/SM2000v191n11ABEH000524
Baer, R. (1964). Irreducible groups of automorphisms of Abelian groups. Pacific J. Math., 14, pp. 385-406. doi: https://doi.org/10.2140/pjm.1964.14.385
Zaitsev, D. I. (1980). Products of Abelian groups. Algebra and Logic, 19, No. 2, pp. 94-106. doi: https://doi.org/10.1007/BF01669835
Brown, K. A. (1982). The Nullstellensatz for certain group rings. J. London Math. Soc., 26, No. 2, pp. 425-434. doi: https://doi.org/10.1112/jlms/s2-26.3.425
Tushev, A. V. (2002). On solvable groups with proper quotient groups of finite rank. Ukr. Math. J., 54, No. 11, pp. 1897-1905. doi: https://doi.org/10.1023/A:1024052726835
Tushev, A. V. (1999). Induced modules over group algebras of metabelian groups of finite rank. Commun. Algebra, 27, No. 12, pp. 5921-5938. doi: https://doi.org/10.1080/00927879908826798
Farcas, D. R. & Passman, D. S. (1982). Primitive Noetherian group rings. Commun. Algebra, 6, No. 3, pp. 301-315. doi: https://doi.org/10.1080/00927877808822247
Roseblade, J. E. (1978). Prime ideals in group rings of polycyclic groups. Proc. London Math. Soc., 36, No. 3, pp. 385-447. doi: https://doi.org/10.1112/plms/s3-36.3.385
Brown, K. A. (1981). Primitive group rings of soluble groups. Arch. Math., 36, No. 1, pp. 404-413. doi: https://doi.org/10.1007/BF01223718
Brookes, C. J. C. (1985). Ideals in group rings of soluble groups of finite rank. Math. Proc. Cambridge. Philos. Soc., 97, No. 1, pp. 27-49. doi: https://doi.org/10.1017/S0305004100062551
Hall, P. (1959). On the finiteness of certain soluble groups. Proc. London Math. Soc., 9, No. 4, pp. 595-622. doi: https://doi.org/10.1112/plms/s3-9.4.595
McConnell, J. C. (1982). The Nullstellensatz and Jacobson properties for rings of differential operators. J. London Math. Soc., 26, No. 1, pp. 37-42. doi: https://doi.org/10.1112/jlms/s2-26.1.37
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