Neutrosophic Triplets in Neutrosophic Rings
oleh: Vasantha Kandasamy W. B., Ilanthenral Kandasamy, Florentin Smarandache
| Format: | Article |
|---|---|
| Diterbitkan: | MDPI AG 2019-06-01 |
Deskripsi
The neutrosophic triplets in neutrosophic rings <inline-formula> <math display="inline"> <semantics> <mrow> <mo>〈</mo> <mi>Q</mi> <mo>∪</mo> <mi>I</mi> <mo>〉</mo> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mo>〈</mo> <mi>R</mi> <mo>∪</mo> <mi>I</mi> <mo>〉</mo> </mrow> </semantics> </math> </inline-formula> are investigated in this paper. However, non-trivial neutrosophic triplets are not found in <inline-formula> <math display="inline"> <semantics> <mrow> <mo>〈</mo> <mi>Z</mi> <mo>∪</mo> <mi>I</mi> <mo>〉</mo> </mrow> </semantics> </math> </inline-formula>. In the neutrosophic ring of integers <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mo>\</mo> <mo>{</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>}</mo> </mrow> </semantics> </math> </inline-formula>, no element has inverse in <i>Z</i>. It is proved that these rings can contain only three types of neutrosophic triplets, these collections are distinct, and these collections form a torsion free abelian group as triplets under component wise product. However, these collections are not even closed under component wise addition.