Consider the complete lattice of substructures of an algebraic structure, or just submodules of a module, or even just ideals in a commutative ring. Every element of this lattice is a join of »principal« substructures (generated by one element). Is there anything else that is special about the set of principal substructures (or its individual elements) from an order-theoretic point of view?
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
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Apr 09, 2026
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