On Weakly 2-Invo Clean Rings With Some Properties in Graph Theory
The concept of a weakly two-involution clean ring is presented; it is a generalization of two-involution clean ring, which allows the addition of more elements to a ring, which will be observed in its graph theoretic representation. The element in a weakly two-involution clean ring can be expressed...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2025-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/ijmm/3682352 |
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| Summary: | The concept of a weakly two-involution clean ring is presented; it is a generalization of two-involution clean ring, which allows the addition of more elements to a ring, which will be observed in its graph theoretic representation. The element in a weakly two-involution clean ring can be expressed as a sum or difference of two elements, which is an involution and an idempotent. Furthermore, if the involution and idempotent can be taken such that they commute, the ring is called a strongly weakly two-involution clean ring. We give some properties of weakly two-involution clean rings. It is also proven that R is isomorphic to all from Z3 or Z5 or Z7 when R is a weakly two-involution clean ring with 2 belonging to the set of all unit elements in R. In addition, this paper contains several results related to graph theory, including the connectedness, diameter, girth, and order of a complete subgraph of the graphs resulting from a weakly two-involution clean ring. |
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| ISSN: | 1687-0425 |