Block Monoid

The set of all zero-systems of a group G is denoted B(G) and is called the block monoid of G since it forms a commutative monoid under the operation of zero-system addition defined by


The monoid has identity emptyset, the zero-system consisting of no elements.

For a nonempty subset S of G, B(G,S) is defined as the set of all zero-systems of G containing only elements from S. For any subset S of G, B(G,S) is a commutative submonoid of B(G). If context makes it obvious, G is often omitted and B(S) is written.

A zero-system is minimal if it contains no proper zero-systems. The set U(G) is defined as the set of all minimal zero-systems of G.

This entry contributed by Nick Hutzler

Explore with Wolfram|Alpha


Anderson, D. F. and Chapman, S. T. "On the Elasticities of Krull Domains with Finite Cyclic Divisor Class Group." Comm. Alg. 28, 2543-2553, 2000.Chapman, S. T. "On the Davenport Constant, the Cross Number, and Their Applications in Factorization Theory." In Zero-Dimensional Commutative Rings (Ed. D. F. Anderson and D. E. Dobbs). New York: Dekker, pp. 167-190, 1997.

Referenced on Wolfram|Alpha

Block Monoid

Cite this as:

Hutzler, Nick. "Block Monoid." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

Subject classifications