query: Do functions with composition form a ring?
positive_passages.docid: 152013
positive_passages.text: elementary ring proof with composition of functions and addition of functions as operations
negative_passages.docid: 130363
negative_passages.text: Prove composition of two surjections is surjection
negative_passages.docid: 57732
negative_passages.text: Rings of fractions and homomorphisms
negative_passages.docid: 9844
negative_passages.text: Proof composition of analytic functions is analytic
negative_passages.docid: 69728
negative_passages.text: If $f$ divides $g$ in $S[x]$, show that $f$ divides $g$ in $R[x]$ for $R$ a sub-ring of $S$.
negative_passages.docid: 17139
negative_passages.text: Ring of holomorphic functions
negative_passages.docid: 155642
negative_passages.text: Understanding divison by monic polynomial in $R[x]$ where $R$ is an arbitrary ring
negative_passages.docid: 135303
negative_passages.text: Formal power series are a euclidean ring
negative_passages.docid: 22604
negative_passages.text: Can $R \times R$ be isomorphic to $R$ as rings?
negative_passages.docid: 33196
negative_passages.text: show that A(T) is a group under operation of composition of functions
negative_passages.docid: 150911
negative_passages.text: Prove that the ring is Artinian and find a composition series of ideals
negative_passages.docid: 1425
negative_passages.text: The Chinese Remainder Theorem for Rings.
negative_passages.docid: 35222
negative_passages.text: Characterizing units in polynomial rings
negative_passages.docid: 106894
negative_passages.text: If a subring of a ring R has identity, does R also have the identity?
negative_passages.docid: 56156
negative_passages.text: Composition and Onto Functions
negative_passages.docid: 152438
negative_passages.text: Is the composition of two injective functions injective?
negative_passages.docid: 136996
negative_passages.text: Fourier transform of function composition