This article describes a grammar game that is an enjoyable way for students to correct sentences. In Climbing Grammar Mountain, best suited for secondary and university students, learners compete in teams to "climb" a game ...

This paper reports on work done with students enrolled in a Level 4 Certificate of Attainment in English (CAEL) class at the University of Waikato Language Institute in Auckland. The original purpose was to help raise the ...

Students in the Middle East have typically been taught English following traditional, rote learning methods. There has been little time, or little room, within the set curriculum for teachers to enrich their students’ ...

A commutative ring R is said to be a phi-ring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map phi from the total quotient ring T(R) to R localized ...

In this paper, we extend the concept of strong extensions of domains to the context of (commutative) rings with zero-divisors. We show that the theory of strong extensions of rings resembles that of strong extensions of domains.

The purpose of this paper is to introduce two new classes of rings that are closely related to the classes of Dedekind domains and Krull domains. Let H = {R | R is a commutative ring with 1 and Nil(R) is a divided prime ...

Let H = {R | R is a commutative ring and Nil(R) is a divided prime ideal of R}. For a ring R in H with total quotient ring T(R), Let phi be the natural ring homomorphism from T(R) into R_Nil(R). An integral domain R is ...

The martingale problem for superprocesses with parameters (𝛏, Ф, 𝑘) is studied where 𝑘(𝒹𝑠) may not be absolutely continuous with respect to the Lebesgue measure. This requires a generalization of the concept of ...