Multi-polarity is a generalization of the term of vector space, where a semi-field is used instead of a field. In this paper, we deal with a three-polar space over a semi-field of double numbers. We also introduce operations of addition and multiplication such that they form a commutative ring with unit on the three-polar space. Both these operations are isomorphic to some operations on the set $\mathbb{R}^4$.
@article{346,
title = {Three-polar space over the semi-field of double numbers},
journal = {Tatra Mountains Mathematical Publications},
volume = {58},
year = {2014},
doi = {10.2478/tatra.v61i0.346},
language = {EN},
url = {http://dml.mathdoc.fr/item/346}
}
Gregor, Tomáš. Three-polar space over the semi-field of double numbers. Tatra Mountains Mathematical Publications, Tome 58 (2014) . doi : 10.2478/tatra.v61i0.346. http://gdmltest.u-ga.fr/item/346/