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G L n -Invariant tensors and graphs

Martin Markl (2008)

Archivum Mathematicum

We describe a correspondence between GL n -invariant tensors and graphs. We then show how this correspondence accommodates various types of symmetries and orientations.

G r - ( 2 , n ) -ideals in graded commutative rings

Khaldoun Al-Zoubi, Shatha Alghueiri, Ece Y. Celikel (2020)

Commentationes Mathematicae Universitatis Carolinae

Let G be a group with identity e and let R be a G -graded ring. In this paper, we introduce and study the concept of graded ( 2 , n ) -ideals of R . A proper graded ideal I of R is called a graded ( 2 , n ) -ideal of R if whenever r s t I where r , s , t h ( R ) , then either r t I or r s G r ( 0 ) or s t G r ( 0 ) . We introduce several results concerning g r - ( 2 , n ) -ideals. For example, we give a characterization of graded ( 2 , n ) -ideals and their homogeneous components. Also, the relations between graded ( 2 , n ) -ideals and others that already exist, namely, the graded prime ideals,...

Gaussian and Prüfer conditions in bi-amalgamated algebras

Najib Mahdou, Moutu Abdou Salam Moutui (2020)

Czechoslovak Mathematical Journal

Let f : A B and g : A C be two ring homomorphisms and let J and J ' be ideals of B and C , respectively, such that f - 1 ( J ) = g - 1 ( J ' ) . In this paper, we investigate the transfer of the notions of Gaussian and Prüfer rings to the bi-amalgamation of A with ( B , C ) along ( J , J ' ) with respect to ( f , g ) (denoted by A f , g ( J , J ' ) ) , introduced and studied by S. Kabbaj, K. Louartiti and M. Tamekkante in 2013. Our results recover well known results on amalgamations in C. A. Finocchiaro (2014) and generate new original examples of rings possessing these properties.

Generalization of the S -Noetherian concept

Abdelamir Dabbabi, Ali Benhissi (2023)

Archivum Mathematicum

Let A be a commutative ring and 𝒮 a multiplicative system of ideals. We say that A is 𝒮 -Noetherian, if for each ideal Q of A , there exist I 𝒮 and a finitely generated ideal F Q such that I Q F . In this paper, we study the transfer of this property to the polynomial ring and Nagata’s idealization.

Groups with large Noether bound

Kálmán Cziszter, Mátyás Domokos (2014)

Annales de l’institut Fourier

The finite groups having an indecomposable polynomial invariant of degree at least half the order of the group are classified. It turns out that –apart from four sporadic exceptions– these are exactly the groups with a cyclic subgroup of index at most two.

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