Theory of matrix factorizations is useful to study hypersurfaces in commutative algebra. To noncommutative hypersurfaces, which are important objects algebraic geometry, we introduce a notion factorization for an arbitrary nonzero non-unit element ring. First show that the category graded invariant under operation called twist (this result generalization by Cassidy-Conner-Kirkman-Moore). Then g...

1. Introduction This study provides a computer-simulated optimal selection of antecedent of reflexive pronouns based on the Visual C++ computer programming language. The algorithm that I use for this implementation is based on the optimal theoretic approach to the proper interpretation of reflexive pronoun roughly adopted in Moon (1999). I show that the complex behavior of reflexive pronouns ca...

Let R be a commutative noetherian local ring that is not Gorenstein. It is known that the category of totally reflexive modules over R is representation infinite, provided that it contains a non-free module. The main goal of this paper is to understand how complex the category of totally reflexive modules can be in this situation. Local rings (R, m) with m3 = 0 are commonly regarded as the stru...

Although much is known about volitional and reflexive smooth eye movements individually, much less is known about how they are coordinated. It is hypothesized that separate cortico-ponto-cerebellar loops subserve these different types of smooth eye movements. Specifically, the MT-MST-DLPN pathway is thought to be critical for ocular following eye movements, whereas the FEF-NRTP pathway is under...

A reflexive graph is a simple undirected graph where a loop has been added at each vertex. If G and H are reflexive graphs and U ⊆ V (H), then a vertex map f : U → V (G) is called nonexpansive if for every two vertices x, y ∈ U , the distance between f(x) and f(y) in G is at most that between x and y in H . A reflexive graph G is said to have the extension property (EP) if for every reflexive g...

In two recent papers [9, 10] we answered a question raised in the book by Eklof and Mekler [7, p. 455, Problem 12] under the set theoretical hypothesis of ♦א1 which holds in many models of set theory, respectively of the special continuum hypothesis (CH). The objects are reflexive modules over countable principal ideal domains R, which are not fields. Following H. Bass [1] an R-module G is refl...

Recent behavioral data have shown that central nonpredictive gaze direction triggers reflexive shifts of attention toward the gazed-at location (e.g., Friesen & Kingstone, 1998). Friesen and Kingstone suggested that this reflexive orienting effect is unique to biologically relevant stimuli. Three experiments were conducted to test this proposal by comparing the attentional orienting produced by...

In this note, it is proved that over a commutative noetherian henselian non-Gorenstein local ring there are infinitely many isomorphism classes of indecomposable totally reflexive modules, if there is a nonfree cyclic totally reflexive module.

The concept of σ-reflexive semigroups is due to Chacron and Thierrin in 1972. In the present paper we discuss σ-reflexive semigroups with apartness. We prove some fundamental properties of these semigroups.

There are three equivalent definitions of dimension for partially ordered sets. When generating these three definitions to ~'-dimension over an arbitrary class of orders ~, the three definitions diverge. We compare these three definitions and determine certain requirements under which they are equivalent.