Let \mathcal{V} be a variety of algebras with zero. In other words ... the map is a bijection, we say that the variety is ideal-determined. The ... ...
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Consider the variety of groups as a variety of algebras with zero ... The ideals in the variety of groups with zero are precisely the same ... ...
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The variety of Lie rings is the variety of algebras with the operator ... :Category:Property satisfactions for the variety of Lie rings ... ...
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In the variety of groups, viewed as a variety of algebras with zero ... * Variety of groups is ideal-determined: This proves, among other ... ...
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The variety of groups is defined as the variety of all algebras with ... universally quantified. An algebra of this variety is thus a set equipped with ... ...
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universal identities. Thus, groups form a variety of algebras. In a similar ... variety of groups is ideal-determined, variety of Lie rings is ideal ... ...
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* Ideal in a variety with zero ... ...
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In the variety of groups, viewed as a variety of algebras with zero ... must also be an ideal. Further, since the variety of groups is ideal-determined ... ...
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The variety of rings is defined as the variety whose members are rings ... Suppose \mathcal{V} is any subvariety of the variety of rings and ... ...
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classes under \sim. If A belongs to any variety, so does A/\sim, so we can ... algebraic statement for this is that the variety of groups is ideal-determined. ... ...
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* In the variety of groups, every ideal (normal subgroup) is a kernel * In the variety of groups, a congruence is completely determined ... ...
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condition: An I-automorphism in a variety of algebras is an automorphism ... intermediate subalgebra condition: In any variety of algebras, an ideal of ... ...
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Suppose \mathcal{V} is a subvariety of the variety of rings, p is ... subgroups with quotient in a specific variety in a group of prime power order ... ...
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Suppose \mathcal{V} is a variety of algebras, A is an algebra of ... * Normality satisfies intermediate subgroup condition: For the variety ... ...
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more general context of homomorphisms in a variety of algebras. ... In the theory of universal algebra, a variety of algebras is a collection ... ...
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===Viewing this in terms of the variety of groups=== identities. In this language, the variety of groups is given by three ... ...
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In the variety of Lie rings, the analogue to normality is the notion of an ideal of a Lie ring, and the analogue of the commutator operation ... ...
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to the subvariety of abelian Lie rings in the variety of Lie rings.
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| 4 || Kernel of Lie bracket || It is the kernel of the Lie bracket homomorphism ... ...
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# A normal subgroup is a kernel in the variety with zero of groups. # A normal subgroup is an ideal in the variety with zero of groups. ... ...
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* Variety of groups is congruence-permutable: The fact that a join of normal subgroups is normal, combined with the fact that the join of normal ... ...
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