THE PROLONGATION PROBLEM OF RING EXTENSIONS
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Abstract
In this paper, we first state the prolongation problem of ring extensions and show that its data (the triple ) determines a regular E-system. Each extension of this regular E-system is a prolongation of the extension E. Next, we prove the result on the classification of extensions of regular E-systems. Then, we obtain the result on the prolongation problem of a ring extension.
Keywords
Ann-phạm trù, E-hệ chính qui, kéo dài mở rộng vành
Article Details
References
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[2]. R. Brown, C. Spencer (1976), G-groupoids, crossed modules and the fundamental groupoid of a topological group, Proc. Konn. Ned. Akad. v. Wet., 79, 296-302.
[3]. A. M. Cegarra, J. M. Garccía - Calcines, J. A. Ortega (2002), On graded categorical groups and equivariant group extensions, Canad. J. Math., 54 (5), 970-997.
[4]. P. T. Cuc, N. T. Quang (2015), Equivariant crossed modules and cohomology of groups with operators, Bulletin of the Korean Mathematical Society, No.4, Vol 52, pp 1077 – 1095.
[5] Phạm Thị Cúc (2014), Hệ nhân tử trong nhóm phạm trù phân bậc, Luận án tiến sĩ, Đại học Huế.
[6] MacLane S. (1975), Homology, Springer - Verlage Berlin. Heidelberg, New York.
[7] MacLane S. (1958), Extensions and obstructions for rings, Illinois J. Mathematics., 2, 316-345.
[8] Nguyen Tien Quang, Pham Thi Cuc (2007), -split ring extension problem, Ann-categories theory and Hoschild cohomology, Journal of Science of Hanoi National University of Education Natural Sciences, Volume 52, Number 4, 3-12.
[9] N. T. Quang, P. T. Cuc (2012), Crossed bimodules over rings and Shukla cohomology, Math. Commun., 17 No. 2, 575-598.
[10] Nguyễn Tiến Quang (1998), Ann-phạm trù, Luận án tiến sĩ, Hà Nội.
[11] N. T. Quang, N. T. Thuy (2007), Ring extension problem, Shukla cohomology and Ann-category, arXiv:0706.0315 [math.CT].
[12] N. T. Quang, D. D. Hanh (2009), Homological classification of Ann-functors, East-West J. of Mathematics, Vol 11, No 2, 195-210.