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Does the notion of modular lattice have anything to do with the meaning of the word modular, in either English or mathematics?

A finite modular lattice is a finite graded lattice $L$ whose rank function $\rho$ satisfies $$ \rho(x)+\rho(y)=\rho(x\wedge y)+\rho(x\vee y) $$ for all $x,y\in L$. It has some equivalent definitions such like a finite lattice such that $$ x\vee (y\wedge z)=(x\vee y)\wedge z $$ for all $x,y,z\in L$ such that $x\le z$. The word modular means employing or involving a module or modules as the basis of design or construction in English, and relating to modulus in mathematics.

David Wang
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    From https://en.wikipedia.org/wiki/Modular_lattice: "Modular lattices arise naturally in algebra and in many other areas of mathematics. In these scenarios, modularity is an abstraction of the 2nd Isomorphism Theorem. For example, the subspaces of a vector space (and more generally the submodules of a module over a ring) form a modular lattice." I think this is the explanation of the name. – Sam Hopkins Jan 23 '19 at 18:39
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    @SamHopkins The wikipedia article you link to also has a history section, which gives more details about the origin of the name! – Alex Kruckman Jan 23 '19 at 18:41
  • In general algebra, a modular lattice does not always come with a grading. It satisfies a modular law, which was observed by Dedekind to hold for (essentially) lattices of normal subgroups of a group. You might search for the history of modular lattices to answer your question. Gerhard "Dedekind Thought Differently About Them" Paseman, 2019.01.23. – Gerhard Paseman Jan 23 '19 at 18:43
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    You might also be interested in this question and this question about the relationships between various meanings of "modular" in mathematics. – Alex Kruckman Jan 23 '19 at 18:45
  • @SamHopkins Yes that answers it. – David Wang Jan 23 '19 at 19:35
  • @AlexKruckman Thanks for the sources. It looks the question does have a historic answer in Richard Dedekind's work. – David Wang Jan 23 '19 at 19:37
  • @GerhardPaseman Thanks for sharing the non-universality of the grading condition though it is true for finite modular lattices. – David Wang Jan 23 '19 at 19:52

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