Question

Prove that $\Pi_{i \in I} \mathbf{A}_i \cong \Pi_{j \in J} (\Pi_{i \in I_j} \mathbf{A}_i)$ where $\{I_j \ | \ j \in J\}$ is a partition of I.

score 113 · Answer 1 · 2014-09-19 20:43:40

113

Views

Prove that $\Pi_{i \in I} \mathbf{A}_i \cong \Pi_{j \in J} (\Pi_{i \in I_j} \mathbf{A}_i)$ where $\{I_j \ | \ j \in J\}$ is a partition of I.

Published on 19 Sep 2014 - 20:43

score 165 · Answer 2 · 2014-09-20 09:41:37

165

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What does a lattice of the direct power of the two-element chain look like?

Published on 20 Sep 2014 - 9:41

score 259 · Answer 3 · 2014-09-21 14:12:18

259

Views

K-free algebra over $\overline{X}$

Published on 21 Sep 2014 - 14:12

score 629 · Answer 4 · 2014-09-23 17:25:46

629

Views

Birkhoff's completeness theorem

Published on 23 Sep 2014 - 17:25

score 59 · Answer 5 · 2014-09-26 15:46:35

59

Views

A Birkhoff theorem on K-free algebras

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167

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score 173 · Answer 7 · 2014-09-27 10:13:14

173

Views

Existence of countably generated free algebra in the universal class

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score 54 · Answer 8 · 2014-10-05 01:18:44

54

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892

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421

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94

Views

Are $e : 1 \rightarrow X$ and $\mathrm{id}_X : X \rightarrow X$ the only operations of $\mathsf{Grp}$ that are homomorphisms?

Published on 20 Oct 2014 - 18:17

score 303 · Answer 12 · 2014-10-21 02:55:48

303

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score 5.6k · Answer 13 · 2026-03-25 06:04:45

5.6k

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score 218 · Answer 14 · 2014-11-11 18:26:44

218

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Prove the identity in Ring of Integers Modulo Prime

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score 240 · Answer 15 · 2026-03-25 02:31:35

240

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List Question

Prove that $\Pi_{i \in I} \mathbf{A}_i \cong \Pi_{j \in J} (\Pi_{i \in I_j} \mathbf{A}_i)$ where $\{I_j \ | \ j \in J\}$ is a partition of I.

What does a lattice of the direct power of the two-element chain look like?

K-free algebra over $\overline{X}$

Birkhoff's completeness theorem

A Birkhoff theorem on K-free algebras

The concept of K-free algebras

Existence of countably generated free algebra in the universal class

Is there accepted terminology for algebraic structures whose every subalgebra is free?

Algebraic Structures: Does Order Matter?

Showing finite lattices are isomorphic to their sets of ideals.

Are $e : 1 \rightarrow X$ and $\mathrm{id}_X : X \rightarrow X$ the only operations of $\mathsf{Grp}$ that are homomorphisms?

A conjecture in equational logic

Which texts do you recommend to study universal algebra and lattice theory?

Prove the identity in Ring of Integers Modulo Prime

Is this a general structure for constructs?

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