We study a class of algebras associated with linear spaces and its relations with polymatroids and integral posets, i.e. posets supporting homogeneous ASL. We prove that the base ring of a transversal polymatroid is Koszul and describe a new class of integral posets. As a corollary we obtain that every Veronese subring of a polynomial ring is an ASL.

Let R be any subring of the reals. We present a generalization of linear systems on graphs where divisors are R-valued functions on the set of vertices and graph edges are permitted to have nonnegative weights in R. Using this generalization, we provide an independent proof of a Riemann-Roch formula, which implies the Riemann-Roch formula of Baker and Norine.

A unitary commutative ring of characteristic 3 and 3-potent is called a 3-ring. We prove that every polynomial of a 3-ring is uniquely determined by its restriction on the subring {0, 1, 2} (the Verification Theorem). Then we establish an isomorphism between the category of 3-rings and the category of Post algebras of order 3.

In this paper, the explicit form of maximal elements, known as shorted operators, in a subring of a von Neumann regular ring has been obtained. As an application of the main theorem, the unique shorted operator (of electrical circuits) which was introduced by Anderson-Trapp has been derived.

Jacobson's generalization [5, Theorem 8] of Wedderburn's theorem [8] states that an algebraic division algebra over a finite field is commutative. These algebras have the property that some power2 of each element lies in the center. Kaplansky observed in [7] that any division ring, or, more generally, any semisimple ring, in which some power of each element lies in the center is commutative. Ka...

For each nontrivial semisimple Hopf algebra H of dimension sixteen over $\mathbb {C}$ , the smallest inner-faithful representation acting on a quadratic AS regular A 2 or 3, homogeneously and preserving grading, is determined. Each invariant subring AH When also regular, thus providing generalization Chevalley–Shephard–Todd Theorem, we say that reflection for A.

the submodules with the property of the title ( a submodule $n$ of an $r$-module $m$ is called strongly dense in $m$, denoted by $nleq_{sd}m$, if for any index set $i$, $prod _{i}nleq_{d}prod _{i}m$) are introduced and fully investigated. it is shown that for each submodule $n$ of $m$ there exists the smallest subset $d'subseteq m$ such that $n+d'$ is a strongly dense submodule of $m$...

This paper focuses on the set-oriented operations and algebraic structures of soft sets. Relatedly, in this paper, firstly some essential properties $\alpha$-intersection set are investigated, where $\alpha$ is a non-empty subset universal set. Later, by using set, notion set-generated subring ring introduced. The generators intersections products subrings given. Some related about investigated...

This paper introduces the expanded real numbers as an ordered subring of hyperreal number field that does not contain any infinitesimals, and defines set all integrable functions from to numbers. allows identify Dirac delta with a special hyperreal-valued function variable: thus defined is general tool, applicable for mathematical modeling physical systems in which infinitely high densities occ...