# Unification Theories: Examples and Applications

## Abstract

**:**

## 1. Introduction

## 2. Examples of Unification Problems

**Remark**

**1.**

**Remark**

**2.**

**Remark**

**3.**

**Remark**

**4.**

**Remark**

**5.**

**Remark**

**6.**

**Remark**

**7.**

## 3. The Unification of Non-Associative Structures

#### 3.1. UJLA Structures

**Definition**

**1.**

**Remark**

**8.**

**Theorem**

**1.**

**Theorem**

**2.**

**Remark**

**9.**

**Remark**

**10.**

**Remark**

**11.**

**Proof.**

#### 3.2. Yang–Baxter Equations

**Definition**

**2.**

- (i)
- $\alpha =\gamma \ne 0,\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\beta \ne 0$;
- (ii)
- $\beta =\gamma \ne 0,\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\alpha \ne 0$;
- (iii)
- $\alpha =\beta =0,\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\gamma \ne 0$.

#### 3.3. Unification of the Conclusions of Theorems

**Theorem**

**3.**

**Proof.**

**Theorem**

**4.**

**Proof.**

**Remark**

**13.**

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Nichita, F.F. Unification Theories: Examples and Applications. *Axioms* **2018**, *7*, 85.
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Nichita FF. Unification Theories: Examples and Applications. *Axioms*. 2018; 7(4):85.
https://doi.org/10.3390/axioms7040085

**Chicago/Turabian Style**

Nichita, Florin F. 2018. "Unification Theories: Examples and Applications" *Axioms* 7, no. 4: 85.
https://doi.org/10.3390/axioms7040085