## Advances in Operator Theory

- Adv. Oper. Theory
- Volume 3, Number 2 (2018), 374-387.

### Operator algebras associated to modules over an integral domain

#### Abstract

We use the Fock semicrossed product to define an operator algebra associated to a module over an integral domain. We consider the $C^*$-envelope of the semicrossed product, and then consider properties of these algebras as models for studying general semicrossed products.

#### Article information

**Source**

Adv. Oper. Theory, Volume 3, Number 2 (2018), 374-387.

**Dates**

Received: 15 June 2017

Accepted: 20 October 2017

First available in Project Euclid: 15 December 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aot/1513328637

**Digital Object Identifier**

doi:10.15352/AOT.1706-1181

**Mathematical Reviews number (MathSciNet)**

MR3738218

**Zentralblatt MATH identifier**

06848506

**Subjects**

Primary: 47L74

Secondary: 47L40: Limit algebras, subalgebras of $C^*$-algebras

**Keywords**

semicrossed product integral domain module

#### Citation

Duncan, Benton. Operator algebras associated to modules over an integral domain. Adv. Oper. Theory 3 (2018), no. 2, 374--387. doi:10.15352/AOT.1706-1181. https://projecteuclid.org/euclid.aot/1513328637