Results 131 to 140 of about 8,103 (256)
Two elementary commutativity theorems for generalized boolean rings
International Journal of Mathematics and Mathematical Sciences, 1997 In this paper we prove that if R is a ring with 1 as an identity element in which xm−xn∈Z(R) for all x∈R and fixed relatively prime positive integers m and n, one of which is even, then R is commutative.
Vishnu Gupta
doaj +1 more source
On the commutativity of near-rings III [PDF]
Bulletin of the Australian Mathematical Society, 1972 Part of the recent work on near-rings has been concerned with sufficient conditions for near-rings to be commutative. Recently Howard E. Bell proved that if a d.g. near-ring R has an identity and for each x, y in R, there exists an n(x, y) > 1, such that (xy−yx)n(x, y) = xy − yx, then R is a commutative ring.
openaire +3 more sources
Information Dynamics and Learning in Complex Adaptive Systems: Toward a Transdisciplinary Framework
Systems Research and Behavioral Science, Volume 43, Issue 4, Page 1344-1363, July/August 2026.ABSTRACT This article develops a framework for understanding learning and adaptation in complex adaptive systems. Drawing from neuroscience, systems theory, information theory and quantum field theory, it examines how information processing, plasticity and systemic coherence emerge from distributed, nonlinear and feedback‐driven interactions. It argues
Anderson de Souza Sant'Anna
wiley +1 more source
An outer measure on a commutative ring [PDF]
, 2016 We show how to produce a reasonable outer measure on a commutative ring from a given measure on a family of prime ideals of this ring.
Dudzik, D., Skrzyński, M.
core
Tate modules as condensed modules
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract We prove that the category of countable Tate modules over an arbitrary discrete ring embeds fully faithfully into that of condensed modules. If the base ring is of finite type, we characterize the essential image as generated by the free module of infinite countable rank under direct sums, duals and retracts.
Valerio Melani +2 more
wiley +1 more source
S-J-Ideals: A Study in Commutative and Noncommutative Rings
Journal of MathematicsIn this paper, we introduce the concept of S-J-ideals in both commutative and noncommutative rings. For a commutative ring R and a multiplicatively closed subset S, we show that many properties of J-ideals apply to S-J-ideals and examine their ...
Alaa Abouhalaka +2 more
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Cohomology of solvable saturable pro‐p$p$ groups and Lie algebras
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract Let p$p$ be an odd prime and let n∈N$n\in \mathbb {N}$ be an integer. We show that the n-th$n{\text{-th}}$ mod‐p$p$ cohomology of a solvable saturable pro‐p$p$ group is isomorphic to the n-th$n{\text{-th}}$ mod‐p$p$ cohomology of its associated Zp$\mathbb {Z}_p$‐Lie algebra g$\mathfrak {g}$ as an Fp$\mathbb {F}_p$‐vector space.
Oihana Garaialde Ocaña +2 more
wiley +1 more source
Proper 3‐realizability and second cohomology of groups on two generators of finite order
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract Given an (infinite) finitely generated group G$G$, its first cohomology group H1(G;ZG)$H^1(G;{\mathbb {Z}}G)$ is free abelian and “counts” the number of ends of G$G$ which equals 1+rank(H1(G;ZG))$1 + rank (H^1(G;{\mathbb {Z}}G))$. The question whether or not for every finitely presented group G$G$ its second cohomology group H2(G;ZG)$H^2(G ...
Francisco F. Lasheras, R. Roy
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Abelian threefolds with imaginary multiplication
Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.Abstract Let A$A$ be an abelian threefold defined over a number field K$K$ with potential multiplication by an imaginary quadratic field M$M$. Under mild assumptions on K$K$, if A$A$ has signature (2,1) and the multiplication by M$M$ is defined over KM$KM$, we attach to A$A$ an elliptic curve defined over K$K$ with potential complex multiplication by M$
Francesc Fité, Pip Goodman
wiley +1 more source
Effect of Polynomial Identity x[x, y] = (x[x, y])n in the Commutativity of Rings
Journal of Mathematical Extension, 2009 . In this paper we study some sufficient conditions for commutativity of a ring according to Jacobsons’idea. Jacobson proved that if R is a ring satisfying x n = x (n > 1) for each x ∈ R, then R is commutative.
Z. Tabatabaei
doaj