On universal embeddings in matrix rings

On absolutely universal embeddings

It is well known that, given a point-line geometry Γ and a projective embedding ε : Γ → PG(V ), if dim(V ) equals the size of a generating set of Γ, then ε is not derived from any other embedding. Thus, if Γ admits an absolutely universal embedding, then ε is absolutely universal. In this paper, without assuming the existence of any absolutely universal embedding, we give sufficient conditions ...

Differential Polynomial Rings of Triangular Matrix Rings

On Skew Triangular Matrix Rings

For a ring R, endomorphism α of R and positive integer n we define a skew triangular matrix ring Tn(R,α). By using an ideal theory of a skew triangular matrix ring Tn(R,α) we can determine prime, primitive, maximal ideals and radicals of the ring R[x;α]/〈xn〉, for each positive integer n, where R[x;α] is the skew polynomial ring, and 〈xn〉 is the ideal generated by xn.

Towards Universal Paraphrastic Sentence Embeddings

We consider the problem of learning general-purpose, paraphrastic sentence embeddings based on supervision from the Paraphrase Database (Ganitkevitch et al., 2013). We compare six compositional architectures, evaluating them on annotated textual similarity datasets drawn both from the same distribution as the training data and from a wide range of other domains. We find that the most complex ar...

Isometric Embeddings and Universal Spaces

We show that if a separable Banach space Z contains isometric copies of every strictly convex separable Banach space, then Z actually contains an isometric copy of every separable Banach space. We prove that if Y is any separable Banach space of dimension at least 2, then the collection of separable Banach spaces which contain an isometric copy of Y is analytic non Borel.