Displaying similar documents to “Embedding sums of cancellative modes into semimodules”

The algebra of mode homomorphisms

Kira Adaricheva, Anna Romanowska, Jonathan Smith (2014)

Open Mathematics

Similarity:

Modes are idempotent and entropic algebras. While the mode structure of sets of submodes has received considerable attention in the past, this paper is devoted to the study of mode structure on sets of mode homomorphisms. Connections between the two constructions are established. A detailed analysis is given for the algebra of homomorphisms from submodes of one mode to submodes of another. In particular, it is shown that such algebras can be decomposed as Płonka sums of more elementary...

Medial modes and rectangular algebras

Anna Zamojska-Dzienio (2006)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Medial modes, a natural generalization of normal bands, were investigated by Płonka. Rectangular algebras, a generalization of rectangular bands (diagonal modes) were investigated by Pöschel and Reichel. In this paper we show that each medial mode embeds as a subreduct into a semimodule over a certain ring, and that a similar theorem holds for each Lallement sum of cancellative modes over a medial mode. Similar results are obtained for rectangular algebras. The paper generalizes earlier...