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Relevant bibliographies by topics / Bimodules and ideals

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Academic literature on the topic 'Bimodules and ideals'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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Journal articles on the topic "Bimodules and ideals"

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Whelan, E. A. "Normalising elements and radicals, I." Bulletin of the Australian Mathematical Society 39, no. 1 (1989): 81–106. http://dx.doi.org/10.1017/s0004972700028008.

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In this paper we study rings and bimodules with no known one-sided chain conditions, but whose (two-sided) ideals and subbimodules are ‘nicely’ generated. We define bi-noetherian polycentral (BPC) and bi-noetherian polynormal (BPN) rings and bimodules, large classes of (almost always) non-noetherian objects, and put on record the basic facts about them. Any BPC ring is a BPN ring. In the case of rings we reduce their properties to properties of the prime ideals, and study the d.c.c. on (two-sided) ideals. We define both the artinian and bi-artinian radicals of a BPN ring, and use them to show that for BPN rings the intersections of the powers of both the Brown-McCoy and the Jacobson radicals are zero.

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Kosler, Karl A. "LINK CLOSED SETS OF PRIME IDEALS AND STABILITY ON BIMODULES." International Electronic Journal of Algebra 17, no. 17 (2015): 188. http://dx.doi.org/10.24330/ieja.266220.

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Anoussis, M., A. Katavolos, and I. G. Todorov. "Ideals ofA(G)and bimodules over maximal abelian selfadjoint algebras." Journal of Functional Analysis 266, no. 11 (2014): 6473–500. http://dx.doi.org/10.1016/j.jfa.2014.03.018.

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KOSLER, KARL A. "ON SYMMETRIC RADICALS OVER FULLY SEMIPRIMARY NOETHERIAN RINGS." Journal of Algebra and Its Applications 02, no. 03 (2003): 351–64. http://dx.doi.org/10.1142/s021949880300057x.

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Symmetric radicals over a fully semiprimary Noetherian ring R are characterized in terms of stability on bimodules and link closure of special classes of prime ideals. The notion of subdirect irreduciblity with respect to a torsion radical is introduced and is shown to be invariant under internal bonds between prime ideals. An analog of the Jacobson radical is produced which is properly larger than the Jacobson radical, yet satisfies the conclusion of Jacobson's conjecture for right fully semiprimary Noetherian rings.

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Khomenko, Oleksandr, and Volodymyr Mazorchuk. "Structure of Modules Induced from Simple Modules with Minimal Annihilator." Canadian Journal of Mathematics 56, no. 2 (2004): 293–309. http://dx.doi.org/10.4153/cjm-2004-014-5.

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AbstractWe study the structure of generalized Verma modules over a semi-simple complex finite-dimensional Lie algebra, which are induced from simple modules over a parabolic subalgebra. We consider the case when the annihilator of the starting simple module is a minimal primitive ideal if we restrict this module to the Levi factor of the parabolic subalgebra. We show that these modules correspond to proper standard modules in some parabolic generalization of the Bernstein-Gelfand-Gelfand category and prove that the blocks of this parabolic category are equivalent to certain blocks of the category of Harish-Chandra bimodules. From this we derive, in particular, an irreducibility criterion for generalized Verma modules. We also compute the composition multiplicities of those simple subquotients, which correspond to the induction from simple modules whose annihilators are minimal primitive ideals.

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Elias, Ben. "A Diagrammatic Temperley-Lieb Categorification." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–47. http://dx.doi.org/10.1155/2010/530808.

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The monoidal category of Soergel bimodules categorifies the Hecke algebra of a finite Weyl group. In the case of the symmetric group, morphisms in this category can be drawn as graphs in the plane. We define a quotient category, also given in terms of planar graphs, which categorifies the Temperley-Lieb algebra. Certain ideals appearing in this quotient are related both to the 1-skeleton of the Coxeter complex and to the topology of 2D cobordisms. We demonstrate how further subquotients of this category will categorify the irreducible modules of the Temperley-Lieb algebra.

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Losev, Ivan, and Victor Ostrik. "Classification of finite-dimensional irreducible modules over -algebras." Compositio Mathematica 150, no. 6 (2014): 1024–76. http://dx.doi.org/10.1112/s0010437x13007604.

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AbstractFinite $W$-algebras are certain associative algebras arising in Lie theory. Each $W$-algebra is constructed from a pair of a semisimple Lie algebra ${\mathfrak{g}}$ (our base field is algebraically closed and of characteristic 0) and its nilpotent element $e$. In this paper we classify finite-dimensional irreducible modules with integral central character over $W$-algebras. In more detail, in a previous paper the first author proved that the component group $A(e)$ of the centralizer of the nilpotent element under consideration acts on the set of finite-dimensional irreducible modules over the $W$-algebra and the quotient set is naturally identified with the set of primitive ideals in $U({\mathfrak{g}})$ whose associated variety is the closure of the adjoint orbit of $e$. In this paper, for a given primitive ideal with integral central character, we compute the corresponding $A(e)$-orbit. The answer is that the stabilizer of that orbit is basically a subgroup of $A(e)$ introduced by G. Lusztig. In the proof we use a variety of different ingredients: the structure theory of primitive ideals and Harish-Chandra bimodules for semisimple Lie algebras, the representation theory of $W$-algebras, the structure theory of cells and Springer representations, and multi-fusion monoidal categories.

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Bodaghi, A., A. Teymouri, and D. Ebrahimi Bagha. "Derivations on the module extension Banach algebras." Ukrains’kyi Matematychnyi Zhurnal 73, no. 4 (2021): 566–76. http://dx.doi.org/10.37863/umzh.v73i4.240.

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UDC 517.986 We correct some results presented in [M. Eshaghi Gordji, F. Habibian, A. Rejali, <em> Ideal amenability of module extension Banach algebras</em>, Int. J. Contemp. Math. Sci., <strong>2</strong>, No. 5, 213–219 (2007)] and, using the obtained consequences, we find necessary and sufficient conditions for the module extension to be -weakly amenable, where is a closed ideal of the Banach algebra and is a closed -submodule of the Banach -bimodule We apply this result to the module extension where are two Banach -bimodules.

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Ashraf, Mohammad, Nazia Parveen, and Bilal Ahmad Wani. "Generalized Higher Derivations on Lie Ideals of Triangular Algebras." Communications in Mathematics 25, no. 1 (2017): 35–53. http://dx.doi.org/10.1515/cm-2017-0005.

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Abstract Let be the triangular algebra consisting of unital algebras A and B over a commutative ring R with identity 1 and M be a unital (A; B)-bimodule. An additive subgroup L of A is said to be a Lie ideal of A if [L;A] ⊆ L. A non-central square closed Lie ideal L of A is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on A, every generalized Jordan triple higher derivation of L into A is a generalized higher derivation of L into A.

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Kajiwara, Tsuyoshi, Claudia Pinzari, and Yasuo Watatani. "Ideal Structure and Simplicity of theC*-Algebras Generated by Hilbert Bimodules." Journal of Functional Analysis 159, no. 2 (1998): 295–322. http://dx.doi.org/10.1006/jfan.1998.3306.

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Dissertations / Theses on the topic "Bimodules and ideals"

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Nery, Janice. "Sobre fechos de módulos sobre anéis semiprimos e não-singulares." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2002. http://hdl.handle.net/10183/79817.

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Se R é um anel não-singular `a direita e Q é o seu anel maximal de quocientes à direita, existe um teorema que estabelece condições equivalentes para que a envoltória injetiva de um ideal `a direita de R seja um Q-bimódulo ([8]). Este teorema ´e provado usando a ortogonalidade de uma família de ideais. Nesta tese estendemos a ortogonalidade de uma família de ideais para uma família de módulos sobre anéis semiprimos e não-singulares `a direita. Com esta noção estendemos o resultado de [8] acima mencionado, para bimódulos centralizantes sobre anéis semiprimos e não-singulares `a direita.<br>In case R is a right nonsingular ring and Q is its right maximal quotients ring, there is a theorem that gives equivalent conditions for the injective hull of a right ideal of R to be a Q-bimodule ([8]). This theorem is proved using the orthogonality of a family of ideals. In this thesis we extended the orthogonality of a family of ideals to a family of modules over semiprime and right nonsingular rings. With this notion we extend the result of [8] to centralizing bimodules over semiprime and right nonsingular rings.

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Books on the topic "Bimodules and ideals"

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Polcino, Milies César, ed. Groups, algebras and applications: XVIII Latin American Algebra Colloquium, August 3-8, 2009, São Pedro, SP, Brazil. American Mathematical Society, 2011.

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Book chapters on the topic "Bimodules and ideals"

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"Bimodules and Affiliated Prime Ideals." In An Introduction to Noncommutative Noetherian Rings. Cambridge University Press, 2004. http://dx.doi.org/10.1017/cbo9780511841699.011.

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