# Pseudo-norm

From Encyclopedia of Mathematics

A generalization of the concept of an absolute value or norm on a field, involving a weakening of one of the axioms: instead of the condition only is required. An example of a pseudo-norm: in the ring of all real-valued continuous functions defined on the segment a pseudo-norm which is not an absolute value is defined by the formula

Every real finite-dimensional algebra can be given a pseudo-norm.

#### References

[1] | A.G. Kurosh, "Lectures on general algebra" , Chelsea (1963) (Translated from Russian) |

**How to Cite This Entry:**

Pseudo-norm.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Pseudo-norm&oldid=16614

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article