Ladder of Algebraic Structures
Out of clarity this is an &quot;algebra over a field&quot; vs a more general concept of an algebra over a ring. More generally an algebra A, over a ring R, <i>an R-algebra</i>, is a ring A equipped with a map Hom(A,Z(R)). Algebra over a field is a special case. Here&#x27;s a &quot;fun&quot; object for you to consider:<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Field_with_one_element" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Field_with_one_element</a>