TY - JOUR
AU - Mesyan, Zachary
AB - Let R be a ring, M a nonzero left R‐module, Ω an infinite set, and E = EndR (⊕Ω M). Given two subrings S1, S2 ⊆ E, write S1 ≈ S2 if there exists a finite subset U ⊆ E such that 〈 S1 ∪ U 〉 = 〈 S2 ∪ U 〉. We show that if M is simple and Ω is countable, then the subrings of E that are closed in the function topology and contain the diagonal subring of E (consisting of endomorphisms that take each copy of M to itself) fall into exactly two equivalence classes, with respect to the equivalence relation above. We also show that every countable subset of E is contained in a 2‐generator subsemigroup of E.
TI - Endomorphism rings generated using small numbers of elements
JF - Bulletin of the London Mathematical Society
DO - 10.1112/blms/bdl038
DA - 2007-04-01
UR - https://www.deepdyve.com/lp/wiley/endomorphism-rings-generated-using-small-numbers-of-elements-qGDmxCmWgj
SP - 290
EP - 300
VL - 39
IS - 2
DP - DeepDyve
ER -