| Summary: | This paper continues a series of papers on unification constructions. After a short discussion on the Euler’s relation, we introduce a matrix version of the Euler’s relation, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>E</mi><mrow><mo> </mo><mi>I</mi><mo> </mo><mi>π</mi></mrow></msup><mo>+</mo><mi>U</mi><mo>=</mo><mi>O</mi></mrow></semantics></math></inline-formula>. We refer to a related equation, the Yang–Baxter equation, and to Yang–Baxter systems. The most consistent part of the paper is on the unification of rings and Boolean algebras. These new structures are related to the Yang–Baxter equation and to Yang–Baxter systems.
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