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A note on hypervector spaces

Sanjay Roy, Tapas K. Samanta (2011)

Discussiones Mathematicae - General Algebra and Applications

The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few important results like deletion theorem, extension theorem, dimension theorem have been established in this hypervector space.

A note on loops of square-free order

Emma Leppälä, Markku Niemenmaa (2013)

Commentationes Mathematicae Universitatis Carolinae

Let Q be a loop such that | Q | is square-free and the inner mapping group I ( Q ) is nilpotent. We show that Q is centrally nilpotent of class at most two.

A note on simple medial quasigroups

K. K. Ščukin (1993)

Commentationes Mathematicae Universitatis Carolinae

A solvable primitive group with finitely generated abelian stabilizers is finite.

A note on uniserial loops

Jaroslav Ježek, Tomáš Kepka (2010)

Commentationes Mathematicae Universitatis Carolinae

All ordinal numbers α with the following property are found: there exists a loop such that its subloops form a chain of ordinal type α .

A parallelogram configuration condition in nets

Jitka Markvartová (1993)

Archivum Mathematicum

After describing a (general and special) coordinatization of k -nets there are found algebraic equivalents for the validity of certain quadrangle configuration conditions in k -nets with small degree k .

Currently displaying 21 – 40 of 914