factoringia
Factoringia is a fictional mathematical concept that studies the general principles of factorization across algebraic and logical structures. It treats factorization as a formal process, extending beyond integers to rings, modules, and other objects, with emphasis on irreducible components and their interactions with structure-preserving maps.
Originating in speculative fiction and philosophical discussions about computation and mathematics, factoringia is described as a
Core ideas include irreducible elements, units, and factorizations; analogues of unique factorization and divisor theories; factor
In theoretical discussions, factoringia raises questions about cryptographic hardness and the limits of algorithmic decomposition; it
See also: Factorization, Unique factorization domains, Algebra, Computational number theory.