Displaying similar documents to “The abelianization of the Johnson kernel”

Relative Gorenstein injective covers with respect to a semidualizing module

Elham Tavasoli, Maryam Salimi (2017)

Czechoslovak Mathematical Journal

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Let R be a commutative Noetherian ring and let C be a semidualizing R -module. We prove a result about the covering properties of the class of relative Gorenstein injective modules with respect to C which is a generalization of Theorem 1 by Enochs and Iacob (2015). Specifically, we prove that if for every G C -injective module G , the character module G + is G C -flat, then the class 𝒢ℐ C ( R ) 𝒜 C ( R ) is closed under direct sums and direct limits. Also, it is proved that under the above hypotheses the class 𝒢ℐ C ( R ) 𝒜 C ( R ) ...

On the invariance of certain types of generalized Cohen-Macaulay modules under Foxby equivalence

Kosar Abolfath Beigi, Kamran Divaani-Aazar, Massoud Tousi (2022)

Czechoslovak Mathematical Journal

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Let R be a local ring and C a semidualizing module of R . We investigate the behavior of certain classes of generalized Cohen-Macaulay R -modules under the Foxby equivalence between the Auslander and Bass classes with respect to C . In particular, we show that generalized Cohen-Macaulay R -modules are invariant under this equivalence and if M is a finitely generated R -module in the Auslander class with respect to C such that C R M is surjective Buchsbaum, then M is also surjective Buchsbaum. ...

On the nilpotent residuals of all subalgebras of Lie algebras

Wei Meng, Hailou Yao (2018)

Czechoslovak Mathematical Journal

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Let 𝒩 denote the class of nilpotent Lie algebras. For any finite-dimensional Lie algebra L over an arbitrary field 𝔽 , there exists a smallest ideal I of L such that L / I 𝒩 . This uniquely determined ideal of L is called the nilpotent residual of L and is denoted by L 𝒩 . In this paper, we define the subalgebra S ( L ) = H L I L ( H 𝒩 ) . Set S 0 ( L ) = 0 . Define S i + 1 ( L ) / S i ( L ) = S ( L / S i ( L ) ) for i 1 . By S ( L ) denote the terminal term of the ascending series. It is proved that L = S ( L ) if and only if L 𝒩 is nilpotent. In addition, we investigate the basic properties of a...

Special modules for R ( PSL ( 2 , q ) )

Liufeng Cao, Huixiang Chen (2023)

Czechoslovak Mathematical Journal

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Let R be a fusion ring and R : = R be the corresponding fusion algebra. We first show that the algebra R has only one left (right, two-sided) cell and the corresponding left (right, two-sided) cell module. Then we prove that, up to isomorphism, R admits a unique special module, which is 1-dimensional and given by the Frobenius-Perron homomorphism FPdim. Moreover, as an example, we explicitly determine the special module of the interpolated fusion algebra R ( PSL ( 2 , q ) ) : = r ( PSL ( 2 , q ) ) up to isomorphism, where r ( PSL ( 2 , q ) ) is the...

Stratified modules over an extension algebra

Erzsébet Lukács, András Magyar (2018)

Czechoslovak Mathematical Journal

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Let A be a standard Koszul standardly stratified algebra and X an A -module. The paper investigates conditions which imply that the module Ext A * ( X ) over the Yoneda extension algebra A * is filtered by standard modules. In particular, we prove that the Yoneda extension algebra of A is also standardly stratified. This is a generalization of similar results on quasi-hereditary and on graded standardly stratified algebras.

Coherence relative to a weak torsion class

Zhanmin Zhu (2018)

Czechoslovak Mathematical Journal

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Let R be a ring. A subclass 𝒯 of left R -modules is called a weak torsion class if it is closed under homomorphic images and extensions. Let 𝒯 be a weak torsion class of left R -modules and n a positive integer. Then a left R -module M is called 𝒯 -finitely generated if there exists a finitely generated submodule N such that M / N 𝒯 ; a left R -module A is called ( 𝒯 , n ) -presented if there exists an exact sequence of left R -modules 0 K n - 1 F n - 1 F 1 F 0 M 0 such that F 0 , , F n - 1 are finitely generated free and K n - 1 is 𝒯 -finitely generated;...

On twisted group algebras of OTP representation type over the ring of p-adic integers

Leonid F. Barannyk, Dariusz Klein (2016)

Colloquium Mathematicae

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Let ̂ p be the ring of p-adic integers, U ( ̂ p ) the unit group of ̂ p and G = G p × B a finite group, where G p is a p-group and B is a p’-group. Denote by ̂ p λ G the twisted group algebra of G over ̂ p with a 2-cocycle λ Z ² ( G , U ( ̂ p ) ) . We give necessary and sufficient conditions for ̂ p λ G to be of OTP representation type, in the sense that every indecomposable ̂ p λ G -module is isomorphic to the outer tensor product V W of an indecomposable ̂ p λ G p -module V and an irreducible ̂ p λ B -module W.

Some homological properties of amalgamated modules along an ideal

Hanieh Shoar, Maryam Salimi, Abolfazl Tehranian, Hamid Rasouli, Elham Tavasoli (2023)

Czechoslovak Mathematical Journal

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Let R and S be commutative rings with identity, J be an ideal of S , f : R S be a ring homomorphism, M be an R -module, N be an S -module, and let ϕ : M N be an R -homomorphism. The amalgamation of R with S along J with respect to f denoted by R f J was introduced by M. D’Anna et al. (2010). Recently, R. El Khalfaoui et al. (2021) introduced a special kind of ( R f J ) -module called the amalgamation of M and N along J with respect to ϕ , and denoted by M ϕ J N . We study some homological properties of the ( R f J ) -module M ϕ J N . Among...

Lifting the field of norms

Laurent Berger (2014)

Journal de l’École polytechnique — Mathématiques

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Let K be a finite extension of Q p . The field of norms of a p -adic Lie extension K / K is a local field of characteristic p which comes equipped with an action of Gal ( K / K ) . When can we lift this action to characteristic 0 , along with a compatible Frobenius map? In this note, we formulate precisely this question, explain its relevance to the theory of ( ϕ , Γ ) -modules, and give a condition for the existence of certain types of lifts.

n - gr -coherent rings and Gorenstein graded modules

Mostafa Amini, Driss Bennis, Soumia Mamdouhi (2022)

Czechoslovak Mathematical Journal

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Let R be a graded ring and n 1 be an integer. We introduce and study the notions of Gorenstein n -FP-gr-injective and Gorenstein n -gr-flat modules by using the notion of special finitely presented graded modules. On n -gr-coherent rings, we investigate the relationships between Gorenstein n -FP-gr-injective and Gorenstein n -gr-flat modules. Among other results, we prove that any graded module in R -gr (or gr- R ) admits a Gorenstein n -FP-gr-injective (or Gorenstein n -gr-flat) cover and preenvelope,...

Annihilators of local homology modules

Shahram Rezaei (2019)

Czechoslovak Mathematical Journal

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Let ( R , 𝔪 ) be a local ring, 𝔞 an ideal of R and M a nonzero Artinian R -module of Noetherian dimension n with hd ( 𝔞 , M ) = n . We determine the annihilator of the top local homology module H n 𝔞 ( M ) . In fact, we prove that Ann R ( H n 𝔞 ( M ) ) = Ann R ( N ( 𝔞 , M ) ) , where N ( 𝔞 , M ) denotes the smallest submodule of M such that hd ( 𝔞 , M / N ( 𝔞 , M ) ) < n . As a consequence, it follows that for a complete local ring ( R , 𝔪 ) all associated primes of H n 𝔞 ( M ) are minimal.

On n -submodules and G . n -submodules

Somayeh Karimzadeh, Javad Moghaderi (2023)

Czechoslovak Mathematical Journal

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We investigate some properties of n -submodules. More precisely, we find a necessary and sufficient condition for every proper submodule of a module to be an n -submodule. Also, we show that if M is a finitely generated R -module and Ann R ( M ) is a prime ideal of R , then M has n -submodule. Moreover, we define the notion of G . n -submodule, which is a generalization of the notion of n -submodule. We find some characterizations of G . n -submodules and we examine the way the aforementioned notions are related...

Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant

Gwénaël Massuyeau (2012)

Bulletin de la Société Mathématique de France

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Let Σ be a compact connected oriented surface with one boundary component, and let π be the fundamental group of Σ . The Johnson filtration is a decreasing sequence of subgroups of the Torelli group of Σ , whose k -th term consists of the self-homeomorphisms of Σ that act trivially at the level of the k -th nilpotent quotient of π . Morita defined a homomorphism from the k -th term of the Johnson filtration to the third homology group of the k -th nilpotent quotient of π . In this paper, we...

The module of vector-valued modular forms is Cohen-Macaulay

Richard Gottesman (2020)

Czechoslovak Mathematical Journal

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Let H denote a finite index subgroup of the modular group Γ and let ρ denote a finite-dimensional complex representation of H . Let M ( ρ ) denote the collection of holomorphic vector-valued modular forms for ρ and let M ( H ) denote the collection of modular forms on H . Then M ( ρ ) is a -graded M ( H ) -module. It has been proven that M ( ρ ) may not be projective as a M ( H ) -module. We prove that M ( ρ ) is Cohen-Macaulay as a M ( H ) -module. We also explain how to apply this result to prove that if M ( H ) is a polynomial ring, then...

𝒟 n , r is not potentially nilpotent for n 4 r - 2

Yan Ling Shao, Yubin Gao, Wei Gao (2016)

Czechoslovak Mathematical Journal

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An n × n sign pattern 𝒜 is said to be potentially nilpotent if there exists a nilpotent real matrix B with the same sign pattern as 𝒜 . Let 𝒟 n , r be an n × n sign pattern with 2 r n such that the superdiagonal and the ( n , n ) entries are positive, the ( i , 1 ) ( i = 1 , , r ) and ( i , i - r + 1 ) ( i = r + 1 , , n ) entries are negative, and zeros elsewhere. We prove that for r 3 and n 4 r - 2 , the sign pattern 𝒟 n , r is not potentially nilpotent, and so not spectrally arbitrary.

-invariants and Darmon cycles attached to modular forms

Victor Rotger, Marco Adamo Seveso (2012)

Journal of the European Mathematical Society

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Let f be a modular eigenform of even weight k 2 and new at a prime p dividing exactly the level with respect to an indefinite quaternion algebra. The theory of Fontaine-Mazur allows to attach to f a monodromy module D f F M and an -invariant f F M . The first goal of this paper is building a suitable p -adic integration theory that allows us to construct a new monodromy module D f and -invariant f , in the spirit of Darmon. The two monodromy modules are isomorphic, and in particular the two -invariants...

One-parameter contractions of Lie-Poisson brackets

Oksana Yakimova (2014)

Journal of the European Mathematical Society

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We consider contractions of Lie and Poisson algebras and the behaviour of their centres under contractions. A polynomial Poisson algebra 𝒜 = 𝕂 [ 𝔸 n ] is said to be of Kostant type, if its centre Z ( 𝒜 ) is freely generated by homogeneous polynomials F 1 , ... , F r such that they give Kostant’s regularity criterion on 𝔸 n ( d x F i are linear independent if and only if the Poisson tensor has the maximal rank at x ). If the initial Poisson algebra is of Kostant type and F i satisfy a certain degree-equality, then the contraction...