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We will consider unital rings A with free additive group, and want to construct (in ZFC) for each natural number k a family of $ℵ_{k}$ -free A-modules G which are separable as abelian groups with special decompositions. Recall that an A-module G is $ℵ_{k}$ -free if every subset of size $< ℵ_{k}$ is contained in a free submodule (we will refine this in Definition 3.2); and it is separable as an abelian group if any finite subset of G is contained in a free direct summand of G. Despite the fact that such a module G is...

$(ℓ, 0)$ -Carter partitions, their crystal-theoretic behavior and generating function.

Berg, Chris, Vazirani, Monica (2008)

The Electronic Journal of Combinatorics [electronic only]

$𝒯$ -Prime Subsets in Semigroups

Bedřich Pondělíček (1975)

Matematický časopis

$(S_{3}, S_{6})$ -Amalgams IV

Wolfgang Lempken, Christopher Parker, Peter Rowley (2005)

Rendiconti del Seminario Matematico della Università di Padova

$(S_{3}, S_{6})$ -Amalgams V

Wolfgang Lempken, Christopher Parker, Peter Rowley (2007)

Rendiconti del Seminario Matematico della Università di Padova

$(S_{3}, S_{6})$ -Amalgams VI

Wolfgang Lempken, Christopher Parker, Peter Rowley (2007)

Rendiconti del Seminario Matematico della Università di Padova

$(S_{3}, S_{6})$ -Amalgams VII

Wolfgang Lempken, Christopher Parker, Peter Rowley (2008)

Rendiconti del Seminario Matematico della Università di Padova

$𝒯$ -semiring pairs

Jaiung Jun, Kalina Mincheva, Louis Rowen (2022)

Kybernetika

We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting including fractions, integral extensions, and Hilbert's Nullstellensatz. Finally, we study a notion of growth in this context.

$𝐇$ -valued differential forms on $𝐇$

Souček, Vladimír (1984)

Proceedings of the 11th Winter School on Abstract Analysis

$\exists$ -свободные группы.

В.Н. Ремесленников (1989)

Sibirskij matematiceskij zurnal

(0,1) - Matrices and semigroups of ring endomorphisms.

C.J. Maxson (1972)

Semigroup forum

$1 \frac{1}{2}$ -generation of finite simple groups.

Stein, Alexander (1998)

Beiträge zur Algebra und Geometrie

$1$ -cocycles on the group of contactomorphisms on the supercircle $S^{1 | 3}$ generalizing the Schwarzian derivative

Boujemaa Agrebaoui, Raja Hattab (2016)

Czechoslovak Mathematical Journal

The relative cohomology $H_{diff}^{1} (𝕂 (1 | 3), 𝔬𝔰𝔭 (2, 3); 𝒟_{λ, μ} (S^{1 | 3}))$ of the contact Lie superalgebra $𝕂 (1 | 3)$ with coefficients in the space of differential operators $𝒟_{λ, μ} (S^{1 | 3})$ acting on tensor densities on $S^{1 | 3}$ , is calculated in N. Ben Fraj, I. Laraied, S. Omri (2013) and the generating $1$ -cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative $1$ -cocycle $s (X_{f}) = D_{1} D_{2} D_{3} (f) α_{3}^{1 / 2}$ , $X_{f} \in 𝕂 (1 | 3)$ which is invariant with respect to the conformal subsuperalgebra $𝔬𝔰𝔭 (2, 3)$ of $𝕂 (1 | 3)$ . In this work we study the supergroup case. We give an explicit construction of $1$ -cocycles of the group...

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