We study the polynomial equations vanishing on tensors of a given rank. By means of polarization we reduce them to elements A of the group algebra Q[Sn×Sn] and describe explicitely linear equations on the coefficients of A to vanish on tensors of a given rank. Further, we reduce the study to the Schur ring over the group Sn × Sn that arises from the diagonal conjugacy action of Sn. More closely...

Let $alpha$ be an automorphism of a ring $R$. The authors [On skewinverse Laurent-serieswise Armendariz rings, Comm. Algebra 40(1)(2012) 138-156] applied the concept of Armendariz rings to inverseskew Laurent series rings and introduced skew inverseLaurent-serieswise Armendariz rings. In this article, we study on aspecial type of these rings and introduce strongly Armendariz ringsof inverse ske...

For a row finite directed graph E, Kumjian, Pask, and Rae-burn proved that there exists a universal C *-algebra C * (E) generated by a Cuntz-Krieger E-family. In this paper we consider two density problems of invertible elements in graph C *-algebras C * (E), and it is proved that C * (E) has stable rank one, that is, the set of all invertible elements is dense in C * (E) (or in its unitization...

Vaught’s conjecture says that for any countable (complete) first-order theory T, the number of non-isomorphic countable models of T is either countable or 2, where ω is the first infinite cardinal. Vaught’s conjecture for ω-stable theories of modules was proved by Garavaglia [6, Theorem 6]. Buechler proved that Vaught’s conjecture is correct for modules of U-rank 1 [2]. It has been shown that V...