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A **planar ternary ring** (PTR) is a specific type of algebraic structure that generalizes some of the properties of linear algebra to more complex relationships involving three elements. Here are the key aspects of planar ternary rings: 1. **Ternary Operation**: A PTR involves a ternary operation, which means it takes three inputs from the set and combines them according to specific rules or axioms.

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  1. Algebraic structures
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