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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
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Cyclic modules over serial rings
Let $R$ be a serial ring. What can be said about the uniform dimension of cyclic $R$-modules? Specially I would like to know Is it true that every cyclic $R$-module has finite uniform dimension ?