title: Domain and range operations in semigroups and rings

authors: Stokes, Tim E.

subjects: Science & Technology

abstract: A D-semigroup S is a semigroup equipped with an operation D satisfying laws asserting that for a ∈ S, D(a) is the smallest e in some set of idempotents U ⊆ S for which ea = a. D-semigroups correspond to left-reduced U-semiabundant semigroups. The basic properties and many examples of D-semigroups are given. Also considered are D-rings, whose multiplicative semigroup is a D-semigroup. Rickart *-rings provide important examples, and the most general D-rings for which the elements of the form D(a) constitute a lattice under the same meet and join operations as for Rickart *-rings are described.

text: Domain and range operations in semigroups and rings A D-semigroup S is a semigroup equipped with an operation D satisfying laws asserting that for a ∈ S, D(a) is the smallest e in some set of idempotents U ⊆ S for which ea = a. D-semigroups correspond to left-reduced U-semiabundant semigroups. The basic properties and many examples of D-semigroups are given. Also considered are D-rings, whose multiplicative semigroup is a D-semigroup. Rickart *-rings provide important examples, and the most general D-rings for which the elements of the form D(a) constitute a lattice under the same meet and join operations as for Rickart *-rings are described.

year: 2015

title: Relationships first and always: A guide to collaborations with indigenous communities

authors: Gardner-Vandy, K.

abstract: Relationship building between Indigenous communities and scientists must be the foundation of all collaborations. Agencies should fund initiatives in relationship building and create an Office of Tribal relations as a supporting framework (§ 4). Guidelines for relationship building are provided (§ 5).

text: Relationships first and always: A guide to collaborations with indigenous communities Relationship building between Indigenous communities and scientists must be the foundation of all collaborations. Agencies should fund initiatives in relationship building and create an Office of Tribal relations as a supporting framework (§ 4). Guidelines for relationship building are provided (§ 5).

year: 2021

title: Approaching Māori language through meaning: The predominance of Indo-European models of relationships within propositions

authors: Whaanga, Hēmi

subjects: Te reo Māori

abstract: In every language, there are relationships between predicators (such as, for example, 'go'/'haere') and arguments (such as, for example, ‘James'/'Hēmi’). One such relationship that has been proposed is that of agency. Thus, in 'James goes'/ ‘E haere ana a Hēmi’), 'James'/'Hēmi' can be said to be the agent of the action 'go'/'haere'. Much of the international literature on relationships of this type is based on research on English and it has been claimed that the relationships that have been identified are universals. However, there may be differences among languages, differences that are attributable to the fact that different languages encode different ways of perceiving divisions in perceptual space. My aim here is to demonstrate, with reference to a number of different models of predicator/ argument relations, that most of them are based on assumptions that derive from the structure of Indo-European languages, English in particular. In Part 2 of this paper (to appear in a subsequent issue of this Journal), the implications of this discussion will be examined with reference to an analysis of Māori in terms of relationships within propositions.

text: Approaching Māori language through meaning: The predominance of Indo-European models of relationships within propositions In every language, there are relationships between predicators (such as, for example, 'go'/'haere') and arguments (such as, for example, ‘James'/'Hēmi’). One such relationship that has been proposed is that of agency. Thus, in 'James goes'/ ‘E haere ana a Hēmi’), 'James'/'Hēmi' can be said to be the agent of the action 'go'/'haere'. Much of the international literature on relationships of this type is based on research on English and it has been claimed that the relationships that have been identified are universals. However, there may be differences among languages, differences that are attributable to the fact that different languages encode different ways of perceiving divisions in perceptual space. My aim here is to demonstrate, with reference to a number of different models of predicator/ argument relations, that most of them are based on assumptions that derive from the structure of Indo-European languages, English in particular. In Part 2 of this paper (to appear in a subsequent issue of this Journal), the implications of this discussion will be examined with reference to an analysis of Māori in terms of relationships within propositions.

year: 2001-09