## Rocky Mountain Journal of Mathematics

- Rocky Mountain J. Math.
- Volume 49, Number 6 (2019), 1857-1867.

### The comparison properties and large subalgebra are inheritance

Qingzhai Fan, Xiaochun Fang, and Xia Zhao

#### Abstract

Let $A$ be a an infinite dimensional stably finite unital simple separable exact ${\rm C^*}$-algebra. Let $B\subset A$ be a stably large subalgebra in $A$ such that $B$ has $m$-comparison of positive elements property (strong tracial $m$-comparison of positive elements property). Then $A$ has $m$-comparison of positive elements property (strong tracial $m$-comparison of positive elements property).

#### Article information

**Source**

Rocky Mountain J. Math., Volume 49, Number 6 (2019), 1857-1867.

**Dates**

First available in Project Euclid: 3 November 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.rmjm/1572746422

**Digital Object Identifier**

doi:10.1216/RMJ-2019-49-6-1857

**Mathematical Reviews number (MathSciNet)**

MR4027237

**Subjects**

Primary: 46L35: Classifications of $C^*$-algebras 46L05: General theory of $C^*$-algebras 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]

**Keywords**

${\rm C^*}$-algebras large subalgebra Cuntz semigroup

#### Citation

Fan, Qingzhai; Fang, Xiaochun; Zhao, Xia. The comparison properties and large subalgebra are inheritance. Rocky Mountain J. Math. 49 (2019), no. 6, 1857--1867. doi:10.1216/RMJ-2019-49-6-1857. https://projecteuclid.org/euclid.rmjm/1572746422