Results 51 to 60 of about 564 (182)

Idempotents which are products of two nilpotents

Special Matrices
Over any GCD (greatest common divisor) commutative domain we show that the nontrivial 2×22\times 2 idempotent matrices are products of two nilpotent matrices. In order to find explicitly such decompositions, two procedures are described.
Călugăreanu Grigore, Pop Horia F.
doaj   +1 more source

An Idempotent-Based Generalization of Semicommutative Rings

Mathematics
We introduce and study several new classes of rings defined by idempotent conditions. A ring R is called i-semicommutative if (1−ab)aRb(1−ab)=0 whenever ab is a nonzero idempotent. This property lies strictly between semicommutativity and i-reversibility
Muhammad Saad, Majed Zailaee
doaj   +1 more source

Modular analogs of character formulas and minimal lifts of modular forms

Bulletin of the London Mathematical Society, Volume 58, Issue 9, September 2026.
Abstract If f$f$ is a mod‐3 eigenform of weight 2 and level Γ0(ℓ2)$\Gamma _0(\ell ^2)$ for a prime ℓ$\ell$ such that ℓ≡−1(mod3)$\ell \equiv -1 \pmod {3}$, and ℓ$\ell$ is a vexing prime for f$f$, we show that there is no obstruction to finding a minimal lift of f$f$, but that there is an obstruction to finding a nonminimal lift.
Patrick B. Allen, Preston Wake
wiley   +1 more source

The determinal rank idempotents of a matrix

Linear Algebra and its Applications, 1996
Let \({\mathbf M}_R\) be the category of finite matrices over a commutative ring \(R\) with 1. For \(A\in {\mathbf M}_R\) of determinantal rank \(r\) let \({\mathcal I}_r (A)\) be the ideal of \(R\) generated by the \(r\times r\) minors of \(A\). There exists a unique list \((e_1, \dots, e_t)\) of pairwise orthogonal idempotents of \(R\) that sum to 1 ...
openaire   +2 more sources

Idempotent elements determined matrix algebras

Linear Algebra and its Applications, 2011
The algebra \(M_n(R)\) of the \(n\times n\) matrices over \(R\) is considered, where \(R\) is a unital commutative ring with invertible 2. The main result shows that the algebra \(M_n(R)\) is idempotent elements determined, i.e. for any \(R\)-module \(X\) and for any symmetric bilinear map \(\{\cdot,\cdot\}:M_n(R)\times M_n(R)\rightarrow X\), the ...
Wang, Dengyin, Li, Xiaowei, Ge, Hui
openaire   +1 more source

Factorizations in Hecke algebras I: Long‐cycle factorizations and Jucys–Murphy elements

Journal of the London Mathematical Society, Volume 114, Issue 3, September 2026.
Abstract Given a permutation, there is a well‐developed literature studying the number of ways one can factor it into a product of other permutations subject to certain conditions. We initiate the analogous theory for the type‐A$A$ Iwahori–Hecke algebra by generalizing the notion of factorization in terms of the Jucys–Murphy elements.
Jose Bastidas, Sarah Brauner, Mathieu Guay‐Paquet, Alejandro H. Morales, GaYee Park, Franco Saliola   +5 more
wiley   +1 more source

IDEMPOTENTS IN CERTAIN MATRIX RINGS OVER POLYNOMIAL RINGS

International Electronic Journal of Algebra, 2020
Let \(R\) be either a direct sum of two different finite prime fields or a finite ring \(\mathbb{Z}/p^2\mathbb{Z}\) where \(p\) is a prime. The paper describes all idempotents of the ring \(M_2(R[x])\) of \(2\times 2\) matrices over the polynomial ring \(R[x]\). Reviewer's remark. It seems that the description is not complete.
BALMACEDA, Jose Maria P., DATU, Joanne Pauline P.   +1 more
openaire   +4 more sources

Interpolation categories for conformal embeddings

Proceedings of the London Mathematical Society, Volume 133, Issue 3, September 2026.
Abstract In this paper, we give a diagrammatic description of the categories of modules coming from the conformal embeddings V(slN,N)⊂V(soN2−1,1)$\mathcal{V}({\mathfrak{sl}}_{N},N)\subset \mathcal{V}({\mathfrak{so}}_{{N}^{2}-1},1)$. A small variant of this construction (morally corresponding to a conformal embedding of glN${\mathfrak{gl}}_{N}$ level N ...
Cain Edie‐Michell, Noah Snyder
wiley   +1 more source

Idempotent 2x2 matrices over linearly ordered abelian groups [PDF]

Categories and General Algebraic Structures with Applications
In this paper we study multiplicative semigroups of $2\times 2$ matrices over a linearly ordered abelian group with an externally added bottom element. The multiplication of such a semigroup is defined by replacing addition and multiplication by join and
Valdis Laan, Marilyn Kutti
doaj   +1 more source

A family of 512 reverse order laws for generalized inverses of a matrix product: A review

Heliyon, 2020
Reverse order laws for generalized inverses of matrix products are a classic object of study in the theory of generalized inverses. One of the well-known reverse order laws for a matrix product AB is (AB)(i,…,j)=B(s2,…,t2)A(s1,…,t1), where (⋅)(i,…,j ...
Yongge Tian
doaj   +1 more source