title: Radicals of 0-regular algebras

authors: McConnell, N. R.

subjects: mathematics

abstract: We consider a generalisation of the Kurosh--Amitsur radical theory for rings (and more generally multi-operator groups) which applies to 0-regular varieties in which all operations preserve 0. We obtain results for subvarieties, quasivarieties and element-wise equationally defined classes. A number of examples of radical and semisimple classes in particular varieties are given, including hoops, loops and similar structures. In the first section, we introduce 0-normal varieties (0-regular varieties in which all operations preserve 0), and show that a key isomorphism theorem holds in a 0-normal variety if it is subtractive, a property more general than congruence permutability. We then define our notion of a radical class in the second section. A number of basic results and characterisations of radical and semisimple classes are then obtained, largely based on the more general categorical framework of L. M\'arki, R. Mlitz and R. Wiegandt as in [13]. We consider the subtractive case separately. In the third section, we obtain results concerning subvarieties and quasivarieties based on the results of the previous section, and also generalise to subtractive varieties some results for multi-operator group radicals defined by simple equational rules. Several examples of radical and semisimple classes are given for a range of fairly natural 0-normal varieties of algebras, most of which are subtractive.

text: Radicals of 0-regular algebras We consider a generalisation of the Kurosh--Amitsur radical theory for rings (and more generally multi-operator groups) which applies to 0-regular varieties in which all operations preserve 0. We obtain results for subvarieties, quasivarieties and element-wise equationally defined classes. A number of examples of radical and semisimple classes in particular varieties are given, including hoops, loops and similar structures. In the first section, we introduce 0-normal varieties (0-regular varieties in which all operations preserve 0), and show that a key isomorphism theorem holds in a 0-normal variety if it is subtractive, a property more general than congruence permutability. We then define our notion of a radical class in the second section. A number of basic results and characterisations of radical and semisimple classes are then obtained, largely based on the more general categorical framework of L. M\'arki, R. Mlitz and R. Wiegandt as in [13]. We consider the subtractive case separately. In the third section, we obtain results concerning subvarieties and quasivarieties based on the results of the previous section, and also generalise to subtractive varieties some results for multi-operator group radicals defined by simple equational rules. Several examples of radical and semisimple classes are given for a range of fairly natural 0-normal varieties of algebras, most of which are subtractive.

year: 2006

title: Vocabulary games as a memory enhancement device

authors: Chen, Meihua

subjects: Taiwan

abstract: I report here on a study whose aim was to determine whether any long-term vocabulary gains were achieved as the result of participation in a game program involving three vocabulary games based loosely on Poker (Pick Red), Chinese Blind Chess and Gobang. Forty six students from a language college in Taiwan participated in a twenty hour game program involving the creation of English compound words from single English words appearing on game cards and game pieces. A vocabulary test relating to these compounds was administered at the beginning of the program (the pretest), on two occasions during the program, on completion of the program and 45 days after completion of the program (the delayed test). Although the results indicated some vocabulary losses between the end of the program and the delayed test, comparison of pretest and delayed test results indicated significant vocabulary gains.

text: Vocabulary games as a memory enhancement device I report here on a study whose aim was to determine whether any long-term vocabulary gains were achieved as the result of participation in a game program involving three vocabulary games based loosely on Poker (Pick Red), Chinese Blind Chess and Gobang. Forty six students from a language college in Taiwan participated in a twenty hour game program involving the creation of English compound words from single English words appearing on game cards and game pieces. A vocabulary test relating to these compounds was administered at the beginning of the program (the pretest), on two occasions during the program, on completion of the program and 45 days after completion of the program (the delayed test). Although the results indicated some vocabulary losses between the end of the program and the delayed test, comparison of pretest and delayed test results indicated significant vocabulary gains.

year: 2009-09

title: Poster Abstracts

authors: Lapsley, Hilary

subjects: Maori

abstract: These are the poster abstracts from the Proceedings of the National Māori Graduates of Psychology Symposium 2002.

text: Poster Abstracts These are the poster abstracts from the Proceedings of the National Māori Graduates of Psychology Symposium 2002.

year: 2003