Results 141 to 150 of about 568 (161)

Absolute Ideals of Algebraically Compact Abelian Groups

Journal of Mathematical Sciences, 2021
The authors research an absolute ideal of an abelian group \(G\), i.e. subgroups of \(G\) such that there is an ideal in every ring whose additive group coincides with \(G\). The ring is called an AI-ring if any ideal is an absolute ideal of the additive group of this ring.
Kompantseva, E. I., Thuy, Pham Thi Thu
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Commutative ideal extensions of abelian groups

ACM SIGSAM Bulletin, 1999
An element \(x\) in a semigroup \(S\) is Archimedean if for every \(y\in S\) there exist a nonnegative integer \(k\) and \(z\in S\) such that \(kx=y+z\). A commutative semigroup \(E\) is an ideal extension of an Abelian group if and only if \(E\) has an element that is Archimedean and idempotent.
Rosales, J. C., García-Sánchez, P. A., García-García, J. I.   +2 more
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Special ideals in partial abelian monoids

Applied Mathematics-A Journal of Chinese Universities, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yu, Zhijian, Cho, Min-Hyung, Wu, Junde
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Idempotent ideals on abelian groups

Journal of Symbolic Logic, 1984
AbstractAn ideal I defined on a group G is called idempotent if for every A ∈ I, {g ∈ G:Ag−1 ∉ ∈ I} ∈ I. We show that a countably complete idempotent ideal on an abelian group cannot be prime but may have strong saturation properties.
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On Euclidean ideal classes in certain Abelian extensions

Mathematische Zeitschrift, 2019
For an algebraic number field \(K\), let \({\mathcal O}_K\), \({\mathcal O}_K^\times\), and \({\text {Cl}}_K\) be, respectively, its ring of integers, unit group, and class group. Let \(E_K\) be the set of all fractional ideals of \(K\) containing \({\mathcal O}_K\). Assume \({\mathcal O}_K^\times\) is infinite and call its rank the unit rank of \(K\).
Deshouillers, J.-M., Gun, S., Sivaraman, J.   +2 more
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Absolute Nil-Ideals of Abelian Groups

Journal of Mathematical Sciences, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Cevian properties in ideal lattices of Abelian ℓ-groups

Forum Mathematicum, 2021
Abstract We consider the problem of describing the lattices of compact ℓ {\ell} -ideals of Abelian lattice-ordered groups.
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Cohomologies of certain Lie algebras with an Abelian ideal

Russian Mathematical Surveys, 1993
Cohomologies of Lie algebras in the adjoint module appear in studying deformations of Lie algebras. If \(Q\) is a Lie algebra with a multiplication \(f_0\), then the Lie algebra \(Q_t=Q \otimes k[[t]]\) is called a deformation of \(Q\) if \(Q_t\) can be endowed by multiplication \(F_t=f_0 + f_1t+f_2t + \cdots\), where \(f_i:Q \times Q\to Q\) are skew ...
Bakhturin, Yu. A., Pagon, D.
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POSITIVE POLARIZATIONS AND ABELIAN IDEALS IN LIE ALGEBRAS

Mathematics of the USSR-Sbornik, 1981
In this paper a theorem on the relative distribution of an abelian ideal and a positive polarization in a Lie algebra (of general type) is proved. It permits one to extend signficantly the domain of application of a theorem on holomorphically induced representations of Lie groups with an abelian normal subgroup and a criterion for nontriviality of the ...
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Notes on R1-ideals in partial abelian monoids

Algebra Universalis, 2000
A cancellative positive partial abelian monoid (CPAM) is an algebra \(\mathcal P =(P;\oplus ,0)\) of type \((2,0)\) which is a partial commutative monoid satisfying the left cancellation law and \(a\oplus b=0\) implies \(a=0\). The author generalizes effect algebras or \(D\)-posets. Several concepts of ideals are introduced. Especially, an \(R1\)-ideal
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