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Article
Piecewise-Koszul algebras
It is a small step toward the Koszul-type algebras. The piecewise-Koszul algebras are, in general, a new class of quadratic algebras but not the classical Koszul ones, simultaneously they agree with both the c...
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Article
On modules with d-Koszul-type submodules
The so-called weakly d-Koszul-type module is introduced and it turns out that each weakly d-Koszul-type module contains a d-Koszul-type submodule. It is proved that, M ∈ ...
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Article
Algebras with periodic shifts of ext degrees
The so-called λ-Koszul algebra and λ-Koszul module are introduced. We give different equivalent descriptions of the λ-Koszul algebra in terms of its minimal graded projective resolution and the Yoneda Ext-algebra...
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Article
(p, λ)-Koszul algebras and modules
In this paper, the notions of (p, λ)-Koszul algebra and (p, λ)-Koszul module are introduced. Some criteria theorems for a positively graded algebra A to be (p, λ)-Koszul are given. The notion of weakly (p, λ)-Kos...
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Article
Notes on piecewise-Koszul algebras
The relationships between piecewise-Koszul algebras and other “Koszul-type” algebras are discussed. The Yoneda-Ext algebra and the dual algebra of a piecewise-Koszul algebra are studied, and a sufficient condi...
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Article
New criteria for λ-Koszul algebras
The main purpose of this paper is to provide some new criteria for a standard graded algebra A = ⊕ i≥0 A i ...
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Article
Nonpure piecewise-Koszul algebras
In this paper, the notions of nonpure piecewise-Koszul algebra and nonpure piecewise-Koszul module are introduced, which are the “nonpure” version of piecewise-Koszul algebras and modules first introduced in [19]...
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Article
Weakly Koszul-like modules
The Koszul-like property for any finitely generated graded modules over a Koszul-like algebra is investigated and the notion of weakly Koszul-like module is introduced. We show that a finitely generated graded mo...
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Article
Discrete Koszul Algebras
Discrete Koszul algebra, another extension of Koszul algebras, is introduced in this paper. The Yoneda algebra of a discrete Koszul algebra is investigated in detail. As an application, we give a...
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Article
Notes on δ-Koszul Algebras
This paper is a continuous work of δ-Koszul algebras, which were first introduced by Green and Marcos in 2005 (see Green and Marcos, Commun Algebra 33(6):1753–1764, 2005). Let
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Article
Koszul-like algebras and modules
In this paper, the notion of Koszul-like algebra is introduced; this notion generalizes the notion of Koszul algebra and includes some Artin-Schelter regular algebras of global dimension 5 as special examples. Ba...
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Article
Notes on nonpure piecewise-Koszul algebras
Let A = ⊕i≥0 A i be a Noetherian standard graded algebra with finite global dimension, gr ...
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Article
Regulation of bile acid metabolism-related signaling pathways by gut microbiota in diseases
Over the past decade, there has been increasing attention on the interaction between microbiota and bile acid metabolism. Bile acids are not only involved in the metabolism of nutrients, but are also important...
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Article
Detection and Quantification of Water-Soluble Inorganic Chlorine, Bromine and Iodine by MALDI-MS
Halogens are elements in soil and water that occur as organic and inorganic species. Studies have shown that inorganic halogens are closely related to animal and plant life. Matrix-assisted laser desorption/io...