Results 81 to 90 of about 9,361 (158)

Bigeneric initial ideals, diagonal subalgebras and bigraded Hilbert functions

Journal of Pure and Applied Algebra, 2000
Let \(k\) be an infinite field, \(R=k[X_1, \dots, X_n,Y_1, \dots,Y_m]\) the polynomial ring in \(m+n\) variables over \(k\). Consider the grading on \(R\) defined by \(\deg X_i=(1,0)\), \(\deg Y_j=(0,1)\). A bigraded ideal is an ideal of \(R\) homogeneous with respect to this grading.
A. ARAMOVA, K. CRONA, DE NEGRI, EMANUELA
openaire   +3 more sources

When do pseudo‐Gorenstein rings become Gorenstein?

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract We discuss the relationship between the trace ideal of the canonical module and pseudo‐Gorensteinness. In particular, under certain mild assumptions, we show that every positively graded domain that is both pseudo‐Gorenstein and nearly Gorenstein is Gorenstein. As an application, we clarify the relationships among nearly Gorensteinness, almost
Sora Miyashita
wiley   +1 more source

Rough subalgebras of some binary algebras connected with logics

International Journal of Mathematics and Mathematical Sciences, 2005
Properties of rough subalgebras and ideals of some binary algebras playing a central role in the theory of algebras connected with different types of nonclassical logics are described.
Wieslaw A. Dudek, Young Bae Jun
doaj   +1 more source

ad-nilpotent ideals of a Borel subalgebra: generators and duality

Journal of Algebra, 2004
It was shown by Cellini and Papi that an ad-nilpotent ideal determines certain element of the affine Weyl group, and that there is a bijection between the ad-nilpotent ideals and the integral points of a simplex with rational vertices. We give a description of the generators of ad-nilpotent ideals in terms of these elements, and show that an ideal has $
openaire   +3 more sources

Fuzzy Subalgebras And Fuzzy Ideals Of Bci-Algebras With Operators

, 2017
{"references": ["Y. Imai and K. Iseki, \"On axiom system of propositional calculus,\" Proc Aapan Academy, vol. 42, pp. 26-29, 1966.", "K. Iseki, \"On BCI-algebras,\" Math. Sem. Notes, vol. 8, pp.125-130, 1980.", "O.G. Xi, \"Fuzzy BCK-algebras,\" Math Japon, vol. 36, pp. 935-942, 1991.", "Y.B. Jun, S.M. Hong, J. Meng and X.L. Xin, \"Characterizations of
Hu, Yuli, Shaoquan Sun
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Glorious pairs of roots and Abelian ideals of a Borel subalgebra [PDF]

Journal of Algebraic Combinatorics, 2019
Let $\mathfrak g$ be a simple Lie algebra with a Borel subalgebra $\mathfrak b$. Let $ ^+$ be the corresponding (po)set of positive roots and $ $ the highest root. A pair $\{ , '\}\subset ^+$ is said to be glorious, if $ , '$ are incomparable and $ + '= $.
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An Algorithm for Computing Ideals and Conjugacy Classes of Subalgebras of Borel Subalgebras

In this article, we present a constructive procedure for determining all ideals of the Borel subalgebra of a complex semisimple Lie algebra from its root system or, equivalently, its Dynkin diagram. The proposed algorithmic approach has been implemented in Maple.
Asghar, Nimra Sher, Azad, Hassan
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Abelian subalgebras and ideals of maximal dimension in Poisson algebras

Journal of Algebra
This paper studies the abelian subalgebras and ideals of maximal dimension of Poisson algebras $\mathcal{P}$ of dimension $n$. We introduce the invariants $α$ and $β$ for Poisson algebras, which correspond to the dimension of an abelian subalgebra and ideal of maximal dimension, respectively. We prove that these invariants coincide if $α(\mathcal{P}) =
A. Fernández Ouaridi, R.M. Navarro, D.A. Towers   +2 more
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SBE-Algebras via Intuitionistic Fuzzy Structures

Mathematics
The study introduces the concept of intuitionistic fuzzy SBE-subalgebras, ideals, and filters, along with level sets of intuitionistic fuzzy sets within the framework of Sheffer stroke BE-algebras. These concepts are shown to be crucial for understanding
Tahsin Oner, Hashem Bordbar, Neelamegarajan Rajesh, Akbar Rezaei   +3 more
doaj   +1 more source

A characterisation of Lie algebras using ideals and subalgebras

Bulletin of the London Mathematical Society
AbstractWe prove that if, for a non‐trivial variety of non‐associative algebras, every subalgebra of every free algebra is free and is an ideal whenever is an ideal, then this variety coincides with the variety of all Lie algebras.
Vladimir Dotsenko, Xabier García‐Martínez   +1 more
openaire   +4 more sources