Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I ran into conflicting definitions ofintegral domain. Herstein defines a ring where existence of unity for multiplication is NOT assumed. His definition of integral domain is:

"A commutative ring R is an integral domain if ab=0 in R implies a=0 or b=0"

I looked in 3 other books and on the Internet, and everywhere either integral domain is defined to contain a multiplicative unit element, or definition of a ring assumes such an element. In either case, integral domain seems to always contain a unit element.

Could someone please explain to me why are there two different definitions and which one is more common?

Thank you.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Definition of integral domain from Herstein

**Physics Forums | Science Articles, Homework Help, Discussion**