ickekommutativa

Ickekommutativa is a term used in some discussions of algebra to denote a relaxed form of commutativity for a binary operation on a set endowed with a partition. In its simplest formulation, a binary operation ⊗ on a set S is called ickekommutativa if S can be partitioned into disjoint blocks B1, B2, … such that for all elements a, b within the same block Bi one has a ⊗ b = b ⊗ a. There is no requirement that elements from different blocks commute with each other. When the partition consists of a single block, the property reduces to ordinary commutativity; if every block yields a commutative substructure, the operation is said to be ickekommutativa on S.

Properties of this notion describe a form of partitioned or block-wise commutativity. It implies that each block forms a commutative subalgebra under ⊗, while non-commutativity can arise from interactions across blocks. The concept is compatible with standard algebraic constructions, such as substructures and products, provided the partition aligns with the block structure.

Examples are typically schematic rather than concrete. A common illustration is to take S as a disjoint union of two sets S1 and S2, with ⊗ defined so that elements within S1 commute with each other and elements within S2 commute with each other, but mixed pairs do not necessarily commute. This yields an ickekommutativa structure without global commutativity.

History and usage: The term is not part of the mainstream algebra canon. It appears mainly in informal writings and niche glossaries as a way to describe partitioned or block-wise commutativity, rather than as a widely standardized axiom.