Partial quotients of moment-angle complexes are topological analogues smooth, not necessarily compact toric varieties. In 1998, Buchstaber and Panov proposed a formula for the cohomology ring such partial quotient in terms torsion product involving corresponding Stanley-Reisner ring. We show that their gives correct cup if 2 is invertible chosen coefficient ring, but general. rectify this by de...

Dade [D1, Theorem 7.4] obtained an important result on the equivalence of categories, extending the classical stable Clifford theory. He used the theory of strongly graded rings. Recently, this work has been generalized to arbitrary graded rings, see E. Dade [D2], [D3], J.L. Gómez Pardo and C. Nǎstǎsescu [GN ], C. Nǎstǎsescu and F. Van Oystaeyen [NVO2]. In the classical case the stable Clifford...

The classical coinvariant ring $$R_n$$ is defined as the quotient of a polynomial in n variables by positive-degree $$S_n$$ -invariants. It has known basis that respects decomposition into irreducible -modules, consisting higher Specht polynomials due to Ariki, Terasoma, and Yamada (Hiroshima Math J 27(1):177–188, 1997). We provide an extension generalized rings $$R_{n,k}$$ introduced Haglund e...

Let R be a G-graded ring and M be a G-graded R-module. In this article, we introduce the concept of graded weakly classical prime submodules and give some properties of such submodules.

An M-polysymmetrical hyperring $(R,+,cdot )$ is an algebraic system, where $(R,+)$ is an M-polysymmetrical hypergroup, $(R,cdot )$ is a semigroup and $cdot$ is bilaterally distributive over $+$. In this paper, we introduce the concept of hyperideals of an M-polysymmetrical hyperring and by using this concept, we construct an ordinary quotient ring. Finally, the fundamental theorem of homomorphi...

Shannon’s classical information theory [18] uses probability theory to analyze channels as mechanisms for information flow. In this paper, we generalize results from [14] for binary channels to show how some more modern tools — probabilistic monads and domain theory in particular — can be used to model classical channels. As initiated in [14], the point of departure is to consider the family of...

Structure theorems are obtained for some classes of modules over the ring of pseudorational numbers and some classes of quotient divisible mixed groups.