Ring extension problem, Shukla cohomology and Ann-category theory

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dc.creatorQuang, Nguyen Tien
dc.creatorThuy, Nguyen Thu
dc.date2007-06-03
dc.date.accessioned2026-07-07T08:03:59Z
dc.date.available2026-07-07T08:03:59Z
dc.descriptionEvery ring extension of $A$ by $R$ induces a pair of group homomorphisms $\mathcal{L}^{*}:R\to End_\Z(A)/L(A);\mathcal{R}^{*}:R\to End_\Z(A)/R(A),$ preserving multiplication, satisfying some certain conditions. A such 4-tuple $(R,A,\mathcal{L}^{*},\mathcal{R}^{*})$ is called a ring pre-extension. Each ring pre-extension induces a $R$-bimodule structure on bicenter $K_A$ of ring $A,$ and induces an obstruction $k,$ which is a 3-cocycle of $\Z$-algebra $R,$ with coefficients in $R$-bimodule $K_A$ in the sense of Shukla. Each obstruction $k$ in this sense induces a structure of a regular Ann-category of type $(R,K_A).$ This result gives us the first application of Ann-category in extension problems of algebraic structures, as well as in cohomology theories.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/0706.0315
dc.identifierhttp://arxiv.org/abs/0706.0315
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/129782
dc.subjectCategory Theory
dc.subject18D10, 18G60, 16E40
dc.titleRing extension problem, Shukla cohomology and Ann-category theory
dc.typetext

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