Perpendicularity in an Abelian Group
We give a set of axioms to establish a perpendicularity relation in an Abelian group and then study the existence of perpendicularities in (ℤn,+) and (ℚ+,·) and in certain other groups. Our approach provides a justification for the use of the symbol ⊥ denoting relative primeness in number theory and...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2013/983607 |
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| Summary: | We give a set of axioms to establish a perpendicularity relation in an Abelian group and
then study the existence of perpendicularities in (ℤn,+) and (ℚ+,·)
and in certain other groups. Our approach provides a justification for the use of the symbol ⊥
denoting relative primeness in number theory and extends the domain of this
convention to some degree. Related to that, we also consider
parallelism from an axiomatic perspective. |
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| ISSN: | 0161-1712 1687-0425 |