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Definition: Existence of an Inverse Element

Let $(X,\ast)$ be an algebraic structure and let $x\in X$. If $e$ denotes the neutral element, an element $y\in X$ with

If $y$ is both, left-inverse and right-inverse, it is called an inverse element of $x$. If such $y$ exists, then we call the element $x$ invertible.

Notes

| | | | | created: 2014-06-08 22:39:00 | modified: 2020-06-27 08:20:22 | by: bookofproofs | references: [577], [7896]

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Bibliography (further reading)

[7896] Fischer, Gerd: “Lehrbuch der Algebra”, Springer Spektrum, 2017, 4. Auflage

[577] Knauer Ulrich: “Diskrete Strukturen – kurz gefasst”, Spektrum Akademischer Verlag, 2001