Displaying similar documents to “When does the F -signature exist?”

Associated graded rings and connected sums

H. Ananthnarayan, Ela Celikbas, Jai Laxmi, Zheng Yang (2020)

Czechoslovak Mathematical Journal

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In 2012, Ananthnarayan, Avramov and Moore gave a new construction of Gorenstein rings from two Gorenstein local rings, called their connected sum. In this article, we investigate conditions on the associated graded ring of a Gorenstein Artin local ring Q , which force it to be a connected sum over its residue field. In particular, we recover some results regarding short, and stretched, Gorenstein Artin rings. Finally, using these decompositions, we obtain results about the rationality...

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,...

n -strongly Gorenstein graded modules

Zenghui Gao, Jie Peng (2019)

Czechoslovak Mathematical Journal

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Let R be a graded ring and n ≥ 1 an integer. We introduce and study n -strongly Gorenstein gr-projective, gr-injective and gr-flat modules. Some examples are given to show that n -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules need not be m -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules whenever n > m . Many properties of the n -strongly Gorenstein gr-injective and gr-flat modules are discussed, some known results are generalized....

About G-rings

Najib Mahdou (2017)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we are concerned with G-rings. We generalize the Kaplansky’s theorem to rings with zero-divisors. Also, we assert that if R ⊆ T is a ring extension such that m T ⊆ R for some regular element m of T , then T is a G-ring if and only if so is R . Also, we examine the transfer of the G-ring property to trivial ring extensions. Finally, we conclude the paper with illustrative examples discussing the utility and limits of our results.

On the structure of sequentially Cohen-Macaulay bigraded modules

Leila Parsaei Majd, Ahad Rahimi (2015)

Czechoslovak Mathematical Journal

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Let K be a field and S = K [ x 1 , ... , x m , y 1 , ... , y n ] be the standard bigraded polynomial ring over K . In this paper, we explicitly describe the structure of finitely generated bigraded “sequentially Cohen-Macaulay” S -modules with respect to Q = ( y 1 , ... , y n ) . Next, we give a characterization of sequentially Cohen-Macaulay modules with respect to Q in terms of local cohomology modules. Cohen-Macaulay modules that are sequentially Cohen-Macaulay with respect to Q are considered.

CF-modules over commutative rings

Ahmed Najim, Mohammed Elhassani Charkani (2018)

Commentationes Mathematicae Universitatis Carolinae

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Let R be a commutative ring with unit. We give some criterions for determining when a direct sum of two CF-modules over R is a CF-module. When R is local, we characterize the CF-modules over R whose tensor product is a CF-module.

Rings consisting entirely of certain elements

Huanyin Chen, Marjan Sheibani, Nahid Ashrafi (2018)

Czechoslovak Mathematical Journal

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We completely determine when a ring consists entirely of weak idempotents, units and nilpotents. We prove that such ring is exactly isomorphic to one of the following: a Boolean ring; ℤ 3 ⊕ ℤ 3 ; ℤ 3 ⊕ B where B is a Boolean ring; local ring with nil Jacobson radical; M 2 ( ℤ 2 ) or M 2 ( ℤ 3 ) ; or the ring of a Morita context with zero pairings where the underlying rings are ℤ 2 or ℤ 3 .

Commutative graded- S -coherent rings

Anass Assarrar, Najib Mahdou, Ünsal Tekir, Suat Koç (2023)

Czechoslovak Mathematical Journal

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Recently, motivated by Anderson, Dumitrescu’s S -finiteness, D. Bennis, M. El Hajoui (2018) introduced the notion of S -coherent rings, which is the S -version of coherent rings. Let R = ⨁ α ∈ G R α be a commutative ring with unity graded by an arbitrary commutative monoid G , and S a multiplicatively closed subset of nonzero homogeneous elements of R . We define R to be graded- S -coherent ring if every finitely generated homogeneous ideal of R is S -finitely presented. The purpose of this paper is to give...

A generalization of reflexive rings

Mete Burak Çalcı, Huanyin Chen, Sait Halıcıoğlu (2024)

Mathematica Bohemica

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We introduce a class of rings which is a generalization of reflexive rings and J -reversible rings. Let R be a ring with identity and J ( R ) denote the Jacobson radical of R . A ring R is called J -reflexive if for any a , b ∈ R , a R b = 0 implies b R a ⊆ J ( R ) . We give some characterizations of a J -reflexive ring. We prove that some results of reflexive rings can be extended to J -reflexive rings for this general setting. We conclude some relations between J -reflexive rings and some related rings. We investigate some extensions...

Left EM rings

Jongwook Baeck (2024)

Czechoslovak Mathematical Journal

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Let R [ x ] be the polynomial ring over a ring R with unity. A polynomial f ( x ) ∈ R [ x ] is referred to as a left annihilating content polynomial (left ACP) if there exist an element r ∈ R and a polynomial g ( x ) ∈ R [ x ] such that f ( x ) = r g ( x ) and g ( x ) is not a right zero-divisor polynomial in R [ x ] . A ring R is referred to as left EM if each polynomial f ( x ) ∈ R [ x ] is a left ACP. We observe the structure of left EM rings with various properties, and study the relationships between the one-sided EM condition and other standard ring theoretic conditions....