Zobrazeno 1 - 10
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pro vyhledávání: '"Bergman, George"'
Autor:
Bergman, George M.
If $\mathcal{C}$ is a category of algebras closed under finite direct products, and $M_\mathcal{C}$ the commutative monoid of isomorphism classes of members of $\mathcal{C},$ with operation induced by direct product, A.Tarski defines a nonidentity el
Externí odkaz:
http://arxiv.org/abs/2409.15541
Autor:
Bergman, George M.
For $P$ a poset, the dimension of $P$ is defined to be the least cardinal $\kappa$ such that $P$ is embeddable in a direct product of $\kappa$ totally ordered sets. We study the behavior of this function on finite-dimensional (not necessarily finite)
Externí odkaz:
http://arxiv.org/abs/2312.12615
Autor:
Bergman, George M.
Let $R$ be a ring, and consider a left $R$-module given with two (generally infinite) direct sum decompositions, $A\oplus(\bigoplus_{i\in I} C_i)=M=B\oplus(\bigoplus_{j\in J} D_j),$ such that the submodules $A$ and $B$ and the $D_j$ are each finitely
Externí odkaz:
http://arxiv.org/abs/2208.06511
Autor:
Bergman, George M.
F. Wehrung has asked: Given a family $\mathcal{C}$ of subsets of a set $\Omega$, under what conditions will there exist a total ordering on $\Omega$ under which every member of $\mathcal{C}$ is convex? Note that if $A$ and $B$ are nondisjoint convex
Externí odkaz:
http://arxiv.org/abs/2011.07399
Autor:
Bergman, George M.
Suppose we wish to embed an (associative) $k$-algebra $A$ in a $k$-algebra $R$ generated in some specified way; e.g., by two elements, or by copies of given $k$-algebras $A_1,$ $A_2,$ $A_3.$ Several authors have obtained sufficient conditions for suc
Externí odkaz:
http://arxiv.org/abs/2011.01448
Autor:
Bergman, George M.
Publikováno v:
Communications in Algebra, 49 (2021) 2516-2537
We review the definition of a quandle, and in particular of the core quandle $\mathrm{Core}(G)$ of a group $G$, which consists of the underlying set of $G$, with the binary operation $x\lhd y = x y^{-1} x$. This is an involutory quandle, i.e., satisf
Externí odkaz:
http://arxiv.org/abs/2006.00641
Autor:
Bergman, George M.
Publikováno v:
Journal of the Iranian Mathematical Society, 1 (2020) 157-161
In Question 19.35 of the Kourovka Notebook, M. H. Hooshmand asks whether, given a finite group $G$ and a factorization $\mathrm{card}(G)= n_1\ldots n_k$, one can always find subsets $A_1,\ldots,A_k$ of $G$ with $\mathrm{card}(A_i)=n_i$ such that $G=A
Externí odkaz:
http://arxiv.org/abs/2003.12866
Autor:
Bergman, George M.
Publikováno v:
Communications in Algebra, 49 (2021) 3760-3776
For which groups $G$ is it true that for all fields $k$, every non-monomial element of the group algebra $k\,G$ generates a proper $2$-sided ideal? The only groups for which we know this are the torsion-free abelian groups. We would like to know whet
Externí odkaz:
http://arxiv.org/abs/1905.12704
Autor:
Bergman, George M.
This is a collection of questions that I am considering submitting to the next edition of the Kourovka Notebook of open questions in group theory. Most are questions I raised in papers between 1981 and the present; a few are new. I welcome feedback.<
Externí odkaz:
http://arxiv.org/abs/1904.04298