title: On EQ-monoids

authors: Stokes, Tim E.

subjects: mathematics

abstract: An EQ-monoid A is a monoid with distinguished subsemilattice L with 1 2 L and such that any a, b 2 A have a largest right equalizer in L. The class of all such monoids equipped with a binary operation that identifies this largest right equalizer is a variety. Examples include Heyting algebras, Cartesian products of monoids with zero, as well as monoids of relations and partial maps on sets. The variety is 0-regular (though not ideal determined and hence congruences do not permute), and we describe the normal subobjects in terms of a global semilattice structure. We give representation theorems for several natural subvarieties in terms of Boolean algebras, Cartesian products and partial maps. The case in which the EQmonoid is assumed to be an inverse semigroup with zero is given particular attention. Finally, we define the derived category associated with a monoid having a distinguished subsemilattice containing the identity (a construction generalising the idea of a monoid category), and show that those monoids for which this derived category has equalizers in the semilattice constitute a variety of EQ-monoids.

text: On EQ-monoids An EQ-monoid A is a monoid with distinguished subsemilattice L with 1 2 L and such that any a, b 2 A have a largest right equalizer in L. The class of all such monoids equipped with a binary operation that identifies this largest right equalizer is a variety. Examples include Heyting algebras, Cartesian products of monoids with zero, as well as monoids of relations and partial maps on sets. The variety is 0-regular (though not ideal determined and hence congruences do not permute), and we describe the normal subobjects in terms of a global semilattice structure. We give representation theorems for several natural subvarieties in terms of Boolean algebras, Cartesian products and partial maps. The case in which the EQmonoid is assumed to be an inverse semigroup with zero is given particular attention. Finally, we define the derived category associated with a monoid having a distinguished subsemilattice containing the identity (a construction generalising the idea of a monoid category), and show that those monoids for which this derived category has equalizers in the semilattice constitute a variety of EQ-monoids.

year: 2006

title: The Content of the Psychological Work Contract for Frontline Police Officers

authors: Cable, Donald Alfred James

subjects: psychological contract

abstract: Adding to the field of knowledge on the content of the psychological work contract, structured interviews with 35 frontline police officers generated 662 responses relating to the content of the psychological work contract for this employment sector. Analysis of these responses resulted in the development of an initial two-component measure of the contract. One component (17 items) reflected the obligations arising from the promises officers believed the organisation had made to them. The other component (19 items) reflected the obligations arising from the promises officers believed they had made to the organisation. The measure was included in a survey completed by 84 frontline police officers. Factor analysis revealed two factors in each component. For the organisation's obligations component, one factor reflected obligations related more to the organisational environment, whereas the other factor reflected obligations related more to the job environment. For the employee's obligations component, one factor reflected obligations related more to behaviours on the job, whereas the other factor reflected obligations related more to the pursuit of development opportunities. The nature of the relationships that emerged between the psychological contract and the nomological network variables included in the study provide strong support for the validity of this measure of the psychological contract.

text: The Content of the Psychological Work Contract for Frontline Police Officers Adding to the field of knowledge on the content of the psychological work contract, structured interviews with 35 frontline police officers generated 662 responses relating to the content of the psychological work contract for this employment sector. Analysis of these responses resulted in the development of an initial two-component measure of the contract. One component (17 items) reflected the obligations arising from the promises officers believed the organisation had made to them. The other component (19 items) reflected the obligations arising from the promises officers believed they had made to the organisation. The measure was included in a survey completed by 84 frontline police officers. Factor analysis revealed two factors in each component. For the organisation's obligations component, one factor reflected obligations related more to the organisational environment, whereas the other factor reflected obligations related more to the job environment. For the employee's obligations component, one factor reflected obligations related more to behaviours on the job, whereas the other factor reflected obligations related more to the pursuit of development opportunities. The nature of the relationships that emerged between the psychological contract and the nomological network variables included in the study provide strong support for the validity of this measure of the psychological contract.

year: 2012

title: Iarararararī

authors: Maxwell, Te Kahautu

abstract: Poi. Lyrics composed by Raniera Poihipi rāua ko Te Kahautu Maxwell. Musical score composed by Te Kahautu Maxwell, Pixie Rogers, Tama Hata, Raharuha Mitai, Renee Mitai, Maisey Rika, Ramari Sherman, Te Rina Ransfield. Performed by Ōpōtiki Mai Tawhiti (Kapa Haka group) (4mins)

Waiata Tira: Aroha
Whakaeke: Haere mai rā
Mōteatea: Te Pātere a Te Turuki
Poi: Iarararararī
Waiata ā ringa: Taku Mana Māori Motuhake
Haka: Waiwharangi
Whakawātea: Āio

text: Iarararararī Poi. Lyrics composed by Raniera Poihipi rāua ko Te Kahautu Maxwell. Musical score composed by Te Kahautu Maxwell, Pixie Rogers, Tama Hata, Raharuha Mitai, Renee Mitai, Maisey Rika, Ramari Sherman, Te Rina Ransfield. Performed by Ōpōtiki Mai Tawhiti (Kapa Haka group) (4mins)

Waiata Tira: Aroha
Whakaeke: Haere mai rā
Mōteatea: Te Pātere a Te Turuki
Poi: Iarararararī
Waiata ā ringa: Taku Mana Māori Motuhake
Haka: Waiwharangi
Whakawātea: Āio

year: 2020-02-06