Our purpose is to present a number of new facts about the structure of semipositive matrices, involving patterns, spectra and Jordon form, sums and products, and matrix equivalence, etc. Techniques used to obtain the results may be of independent interest. Examples include: any matrix with at least two columns is a sum, and any matrix with at least two rows, a product, of semipositive matrices. Any spectrum of a real matrix with at least 2 elements is the spectrum of a square semipositive matrix, and any real matrix, except for a negative scalar matrix, is similar to a semipositive matrix. M-matrices are generalized to the non-square case and sign patterns that require semipositivity are characterized., Jonathan Dorsey, Tom Gannon, Charles R. Johnson, Morrison Turnansky., and Obsahuje seznam literatury
An S-closed submodule of a module M is a submodule N for which M/N is nonsingular. A module M is called a generalized CS-module (or briefly, GCS-module) if any S-closed submodule N of M is a direct summand of M. Any homomorphic image of a GCS-module is also a GCS-module. Any direct sum of a singular (uniform) module and a semi-simple module is a GCS-module. All nonsingular right R-modules are projective if and only if all right R-modules are GCS-modules., Qingyi Zeng., and Obsahuje seznam literatury
A subgroup H of a finite group G is said to be ss-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K is s-permutable in K. In this paper, we first give an example to show that the conjecture in A.A. Heliel’s paper (2014) has negative solutions. Next, we prove that a finite group G is solvable if every subgroup of odd prime order of G is ss-supplemented in G, and that G is solvable if and only if every Sylow subgroup of odd order of G is ss-supplemented in G. These results improve and extend recent and classical results in the literature., Jiakuan Lu, Yanyan Qiu., and Obsahuje seznam literatury
We study the arithmetic properties of hyperelliptic curves given by the affine equation y^{2} = x^{n} + a by exploiting the structure of the automorphism groups. We show that these curves satisfy Lang’s conjecture about the covering radius (for some special covering maps)., Kevser Aktaş, Hasan Şenay., and Obsahuje seznam literatury