Let $R= \oplus_{ \alpha \in G} R_{\alpha}$ be a commutative ring with unity graded by an arbitrary grading monoid $G$. For each positive integer, the notions of graded-n-coherent module and are introduced. In this paper many results generalized from $n$-coherent rings to graded-$n$-coherent rings. last section, we provide necessary sufficient conditions for trivial extension graded-valuation ri...

The main purpose is to characterise continuous maps that are n-branched coverings in terms of induced maps on the rings of functions. The special properties of Frobenius n-homomorphisms between two function spaces that correspond to n-branched coverings are determined completely. Several equivalent definitions of a Frobenius n-homomorphism are compared and some of their properties are proved. A...

We investigate boundary states of N = 2 coset models based on Grassmannians Gr(n, n+k), and find that the underlying intersection geometry is given by the fusion ring of U (n). This is isomorphic to the quantum cohomology ring of Gr(n, n+k+1), which in turn can be encoded in a " boundary " superpotential whose critical points correspond to the boundary states. In this way the intersection prope...

We study the properties of rings satisfying Auslander-type conditions. If an artin algebra Λ satisfies the Auslander condition (that is, Λ is an ∞-Gorenstein artin algebra), then we construct two kinds of subcategories which form functorially finite cotorsion theories. Noetherian rings satisfying ‘Auslander-type conditions’ on self-injective resolutions can be regarded as certain non-commutativ...

The title compound, {[Zn(C3H3N2)(C3H4N2)2]NO3} n , is a one-dimensional coordination polymer along [01-1] with the Zn(II) atom coordinating to four imidazole/imidazolide rings. The Zn(II) atom has a regular tetra-hedral geometry with the planes of the two monodentate imidazole rings inclined to one another by 87.94 (17)°, while the planes of the bridging imidazolide rings are inclined to one an...

Decomposability of an algebraic structure into the union of its sub-structures goes back to G. Scorza's Theorem of 1926 for groups. An analogue of this theorem for rings has been recently studied by A. Lucchini in 2012. On the study of this problem for non-group semigroups, the first attempt is due to Clifford's work of 1961 for the regular semigroups. Since then, N.P. Mukherjee in 1972 studied...

The Pythagoras number of a ring A is the smallest integer p A = p ≥ 1 such that any sum of squares of A is a sum of p squares, and p A = +∞ if such an integer does not exist. This is a very delicate invariant whose study has deserved a lot of attention from specialists in number theory, quadratic forms, real algebra, and real geometry. Wellknown examples are the following: p = 4 (Lagrange’s fam...