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A UNIFORM COHOMOLOGY THEORY FOR ALGEBRAS. [PDF]

Proc Natl Acad Sci U S A, 1964
Gerstenhaber M.
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Groups, Categories and Duality. [PDF]

Proc Natl Acad Sci U S A, 1948
Maclane S.
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Schwarz'S lemma in normed linear spaces. [PDF]

Proc Natl Acad Sci U S A, 1969
Harris LA.
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Splittable Jordan homomorphisms and commutator ideals

Journal of Algebra
We define a Jordan homomorphism $φ$ from a ring $R$ to a ring $R'$ to be splittable if the ideal (of the subring generated by the image of $φ$) generated by all $φ(xy)-φ(x)φ(y)$, $x,y\in R$, has trivial intersection with the ideal generated by all $φ(xy)-φ(y)φ(x)$, $x,y\in R$. Our main result states that a splittable Jordan homomorphism is the sum of a
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FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES. [PDF]

Proc Natl Acad Sci U S A, 1963
Lawvere FW.
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Dependent Probabilities and Spaces (L). [PDF]

Proc Natl Acad Sci U S A, 1938
Birkhoff G.
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Sets of lengths in maximal orders in central simple algebras.

J Algebra, 2013
Smertnig D.
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Jordan homomorphisms and derivations on semisimple Banach algebras. [PDF]

Proceedings of the American Mathematical Society, 1970
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Jordan homomorphisms of operator algebras

, 1964
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Characterizations of Jordan derivations and Jordan homomorphisms

Linear and Multilinear Algebra, 2011
Let 𝒜 be a unital Banach algebra and ℳ be a unital 𝒜-bimodule. We show that if δ is a linear mapping from 𝒜 into ℳ satisfying δ(ST) = δ(S)T +Sδ(T) for any S, T ∈ 𝒜 with ST = W, where W is a left or right separating point of ℳ, then δ is a Jordan derivation.
Jiankui Li, Jiren Zhou
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