Regularity and Products of Idemopotents in Endmorphism Monoids of Projective Acts

That the monoid of all transformations of any set and the monoid of all endomorphisms of any vector space over a division ring are regular (in the sense of von Neumann) has been known for many years (see [6] and [16], respectively). A common generalization of these results to the endomorphism monoid of an independence algebra can be found in [13]. It also follows from [13] that the endomorphism monoid of a free G-act is regular, where G is any group. In the present paper we use a version of the wreath product construction of [8], [9] to determine the projective right S-acts (S any monoid) whose endomorphism monoid is regular

Flatness Properties of Acts over Commutative, Cancellative Monoids

This note presents a classification of commutative, cancellative monoids S by flatness properties of their associated S-acts

On Congruence Compact Monoids

A universal algebra is called congruence compact if every family of congruence classes with the finite intersection property has a non-empty intersection. This paper determines the structure of all right congruence compact monoids S for which Green’s relations J and H coincide. The results are thus sufficiently general to describe, in particular, all congruence compact commutative monoids and all right congruence compact Clifford inverse monoids

Carbohydrate-derived iminium salt organocatalysts for the asymmetric epoxidation of alkenes

A new family of carbohydrate-based dihydroisoquinolinium salts has been prepared and tested for potential as asymmetric catalysts for the epoxidation of unfunctionalized alkene substrates, providing up to 57% ee in the product epoxides

Monoids over which all weakly flat acts are flat

If R is a ring with identity and M is a left R-module then it is well known that the following statements are equivalent: (1) M is flat. (2) The functor—⊗ M preserves embeddings of right ideals into R. This paper investigates situations in which the analogous statements are equivalent in the context of S-sets over a monoid S

How making entrance exams more accessible can increase college attendance

Despite being academically ready, many students fail to take a college entrance exam. In new research, George Bulman finds that this may be due in part to differing access to such exams from school to school and state to state. He finds that new testing centres are likely to increase SAT test taking rates by 4 percentage point for those students who live nearby. He writes that, especially for high ability students, increasing access to exams makes it is much more likely that they will continue on to, and complete, a four-year college education

Effective Phonemic Awareness Instruction for Increased Reading Achievement

Reading fluently and for meaning is an essential skill that has allowed students to function effectively in society. Throughout the years, the reading achievement gap has continued to widen and linger across the United States. The low rates of literacy represent a national crisis, especially for low-income Americans. Research shows that strong phonemic awareness instruction and early intervention in the primary grades are key to closing the reading achievement gap. This paper explores the reasons behind the reading achievement gap and what differentiated instructional strategies early educators can employ to support students in the acquisition of skills such as phonemic awareness, alphabet recognition, and vocabulary development. A diverse selection of literature, as well as quantitative and qualitative research studies, were reviewed to determine how solid, proactive differentiated phonics instruction with reading will help educators effectively enhance the student’s ability to learn and have access to content through their ability to read fluently. This paper seeks to answer the research question: In light of what is known about differentiated instruction, how do phonics instruction and intervention impact reading achievement and close the reading achievement gap with students who are performing below grade level in the primary grades