A first course in noncommutative rings

By B. Denton. Mathematical Gazette, 2002

2,294 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/afbda45105eab1692aa77e4e1a06860d2b4f41b8

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Citations in the corpus

The $p$-Canonical Basis for Hecke Algebras (2015, positive): “Since EndH(Bw) is a finitely generated O-module, we can use idempotent lifting techniques for complete local rings (see [Lam01, Theorem 21.31]) and find an idempotent ẽ ∈ EndH(Bw) mapping to e in EndkH(Bw ⊗O k) ≅ EndH(Bw) ⊗O k.”
Pseudo Drazin inverses in associative rings and Banach algebras (2012, background): “For other unexplained terms in ring theory and Banach algebras, see [13,18].”
Rings with Property (A) and their extensions (2007, background): “Note that x 1 ··· x n (cid:5)= 0 because P is completely prime by [16, Lemma 12.6].”
A taxonomy of 2-primal rings (2003, methodology): “We follow the notation, conventions, and nomenclature of [37] and [39].”
On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation (2015, methodology): “We will use the well-known fact that a one-sided ideal in which every element is quasi-regular generates a two-sided ideal which is Jacobson radical [34].”
POOR MODULES: THE OPPOSITE OF INJECTIVITY (2010, background): “Other good references are [6], [11] and [20].”
Coordinate Algebras of Extended Affine Lie Algebras of Type A1 (2000, background): “Both statements are well-known for the associative case (see [11] p.”
Rings in which every element is either a sum or a difference of a nilpotent and an idempotent (2014, background): “All other unexplained explicitly below notion and notation are standard and follow essentially those from [14].”
Power series and analyticity over the quaternions (2009, background): “Hence the theory of regular quaternionic functions, which is quickly developing, reveals a new feature that reminds the nice properties of holomorphic complex functions.”
On Some Properties of the Quaternionic Functional Calculus (2009, background): “The statement follows from the factorization theorem, see [18], and the fact that the second degree polynomial q2 − 2Re[s]q + |s|2 has real coefficients.”