A Noetherian integral domain R is said to be a splinter if it is a direct summand, as an R–module, of every module–finite extension ring, see [Ma]. In the case that R contains the field of rational numbers, it is easily seen that R is splinter if and only if it is a normal ring, but the notion is more subtle for rings of characteristic p > 0. It is known that F–regular rings of characteristic p...

4.3. (i) Since HomA(A (I),M) ∼= M (I) for a set I and ⊕ is exact, it is clear that HomA(A (I),−) is exact, i.e. A(I) is projective. (ii) “Only if” part: Let A(P ) = ⊕ p∈P Ap be the free A-module indexed by P and ψ : A (P ) → p be the A-homomorphism such that ψ(1p) = p. Then ψ is surjective. If P is projective, then ψ has a section, i.e. an A-homomorphism φ : P → A(P ) such that ψ ◦ φ = idP . Th...

Let k be a field and let G be a finite group. By a theorem of D. Benson, H. Krause and S. Schwede, there is a canonical element in the Hochschild cohomology of the Tate cohomology γG ∈ HH 3,−1Ĥ∗(G) with the following property: Given any graded Ĥ∗(G)-module X, the image of γG in Ext 3,−1 Ĥ∗(G) (X,X) is zero if and only if X is isomorphic to a direct summand of Ĥ(G,M) for some kG-module M . Suppo...

A submodule [Formula: see text] of is summand absorbing, if implies for any text]. Such submodules often appear in modules over (additively) idempotent semirings, particularly tropical algebra. This paper studies amalgamation and extensions these submodules, more generally upper bound modules.

According to theorems of C. Gordon, J. Luecke, and W. Parry, if a knot exterior X has two distinct planar boundary slopes r1, r2, then at least one of the manifolds X(r1), X(r2) has a connected summand M with nontrivial torsion in first homology. The 3-manifolds M obtained in this way, which we call t-manifolds, have special Heegaard splittings, or t-manifold structures. In this paper we study ...

We introduce a concept of causality in the framework of generalized pseudo-Riemannian Geometry in the sense of Colombeau. This is motivated by a generalized point value characterization of generalized pseudoRiemannian metrics due to M. Kunzinger et al. We prove an appropriate version of the inverse Cauchy-Schwarz inequality. As an application, we establish a dominant energy condition for some e...

A superdiagonal composition is one in which the i-th part or summand of size greater than equal to i. In this paper, we study number palindromic compositions and colored compositions. particular, give generating functions explicit combinatorial formulas involving binomial coefficients Stirling numbers first kind.

The purpose of this paper is to establish an integral connection between the relative K-theory and cyclic homology of a square-zero ideal IeR, R a ring with unit. We restrict attention to the case when R is a split extension of R/I by I. The outline of the paper is as follows: in Section 2, we compute a direct summand of HC*(R, I), where HC*(R, 1) is graded in analogy to relative K-theory and f...

Let p be prime, and $$n,m \in \mathbb {N}$$ . When K/F is a cyclic extension of degree $$p^n$$ , we determine the $$\mathbb {Z}/p^m\mathbb {Z}[\text {Gal}(K/F)]$$ -module structure $$K^\times /K^{\times p^m}$$ With at most one exception, each indecomposable summand free over some quotient group $$\text {Gal}(K/F)$$ For fixed values m n, there are only finitely many possible isomorphism classes ...