Arithmetic and $k$-maximality of the cyclic free magma

Carles Card\'o

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Arithmetic and $k$-maximality of the cyclic free magma

Carles Cardó

Rings and Algebras · Submitted 25 Jul 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim These two tools, arithmetic and maximality, allow us to study the lattice of the submagmas of a free magma.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,548 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.07 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We survey free magmas and we explore the structure of their submagmas. By equipping the cyclic free magma with a second distributive operation we obtain a ringoid-like structure with some primitive arithmetical properties. A submagma is $k$-maximal when there are only $k-1$ submagmas between it and the free magma itself. These two tools, arithmetic and maximality, allow us to study the lattice of the submagmas of a free magma.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We survey free magmas and we explore the structure of their submagmas.	background 0.58	0.74	0.05	asserted 0.84
s1	By equipping the cyclic free magma with a second distributive operation we obtain a ringoid-like structure with some primitive arithmetical properties.	contribution 0.72	0.87	0.18	asserted 1.00
s2	A submagma is $k$-maximal when there are only $k-1$ submagmas between it and the free magma itself.	background 0.74	0.23	0.07	asserted 0.99
s3	These two tools, arithmetic and maximality, allow us to study the lattice of the submagmas of a free magma.	contribution 0.58	0.68	0.32	asserted 0.98

What kind of paper the classifier reports this is: review 0.39 · evidence from proof or derivation 0.81.

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arXiv listing abstract v1

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We survey free magmas and we explore the structure of their submagmas. By equipping the cyclic free magma with a second distributive operation we obtain a ringoid-like structure with some primitive arithmetical properties. A submagma is $k$-maximal when there are only $k-1$ submagmas between it and the free magma itself. These two tools, arithmetic and maximality, allow us to study the lattice of the submagmas of a free magma.

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