# A survey of s-unital and locally unital rings

@article{Nystedt2018ASO, title={A survey of s-unital and locally unital rings}, author={Patrik Nystedt}, journal={arXiv: Rings and Algebras}, year={2018} }

We gather some classical results and examples that show strict inclusion between the families of unital rings, rings with enough idempotents, rings with sets of local units, locally unital rings, s-unital rings and idempotent rings.

#### 9 Citations

Prime group graded rings with applications to partial crossed products and Leavitt path algebras

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In this article we generalize a classical result by Passman on primeness of unital strongly group graded rings to the class of nearly epsilon-strongly group graded rings which are not necessarily… Expand

The graded structure of algebraic Cuntz-Pimsner rings

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The algebraic Cuntz-Pimsner rings are naturally Z-graded rings that generalize both Leavitt path algebras and unperforated Z-graded Steinberg algebras. We classify strongly, epsilon-strongly and… Expand

Hochschild (Co)homology and Derived Categories

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These are slightly expanded notes of lectures given in April 2019 at the Isfahan school and conference on representations of algebras. We recall the formalism of derived categories and functors and… Expand

The graded structure of algebraic Cuntz-Pimsner rings

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The algebraic Cuntz-Pimsner rings are naturally $\mathbb{Z}$-graded rings that generalize both Leavitt path algebras and unperforated $\mathbb{Z}$-graded Steinberg algebras. We classify strongly,… Expand

A characterization of graded von Neumann regular rings with applications to Leavitt path algebras

- Mathematics
- 2019

We provide a characterization of graded von Neumann regular rings involving the recently introduced class of nearly epsilon-strongly graded rings. As our main application, we generalize Hazrat's… Expand

GRADED MODULES OVER OBJECT-UNITAL GROUPOID GRADED RINGS

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In a previous article (see [6]), we introduced and analyzed ring-theoretic properties of object unital G-graded rings R, where G is a groupoid. In the present article, we analyze the category G-R-mod… Expand

Object-unital groupoid graded modules.

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Given a groupoid $\mathcal{G}$ and an associative but not necessarily unital ring $R$, we introduce the notion of object unital graded ring and construct the category of object unital graded modules… Expand

Induced quotient group gradings of epsilon-strongly graded rings

- Mathematics
- 2018

Let $G$ be a group and let $S=\bigoplus_{g \in G} S_g$ be a $G$-graded ring. Given a normal subgroup $N$ of $G$, there is a naturally induced $G/N$-grading of $S$. It is well-known that if $S$ is… Expand

Object-unital groupoid graded rings, crossed products and separability

- Mathematics
- 2020

Abstract We extend the classical construction by Noether of crossed product algebras, defined by finite Galois field extensions, to cover the case of separable (but not necessarily finite or normal)… Expand

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