31,572 research outputs found

    Infinite partition monoids

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    Let PX\mathcal P_X and SX\mathcal S_X be the partition monoid and symmetric group on an infinite set XX. We show that PX\mathcal P_X may be generated by SX\mathcal S_X together with two (but no fewer) additional partitions, and we classify the pairs α,β∈PX\alpha,\beta\in\mathcal P_X for which PX\mathcal P_X is generated by SX∪{α,β}\mathcal S_X\cup\{\alpha,\beta\}. We also show that PX\mathcal P_X may be generated by the set EX\mathcal E_X of all idempotent partitions together with two (but no fewer) additional partitions. In fact, PX\mathcal P_X is generated by EX∪{α,β}\mathcal E_X\cup\{\alpha,\beta\} if and only if it is generated by EX∪SX∪{α,β}\mathcal E_X\cup\mathcal S_X\cup\{\alpha,\beta\}. We also classify the pairs α,β∈PX\alpha,\beta\in\mathcal P_X for which PX\mathcal P_X is generated by EX∪{α,β}\mathcal E_X\cup\{\alpha,\beta\}. Among other results, we show that any countable subset of PX\mathcal P_X is contained in a 44-generated subsemigroup of PX\mathcal P_X, and that the length function on PX\mathcal P_X is bounded with respect to any generating set

    Idempotents and one-sided units in infinite partial Brauer monoids

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    We study monoids generated by various combinations of idempotents and one- or two-sided units of an infinite partial Brauer monoid. This yields a total of eight such monoids, each with a natural characterisation in terms of relationships between parameters associated to Brauer graphs. We calculate the relative ranks of each monoid modulo any other such monoid it may contain, and then apply these results to determine the Sierpinski rank of each monoid, and ascertain which ones have the semigroup Bergman property. We also make some fundamental observations about idempotents and units in arbitrary monoids, and prove some general results about relative ranks for submonoids generated by these sets. Dedicated to Dr Des FitzGerald on the occasion of his 70th birthday.Comment: To appear in J Algebra. V2 incorporates referee's suggestions: 37 pages; 7 figures; 1 table. V1: 38 pages; 8 figures; 2 table

    Provision of palliative care in Malta

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    The Malta Hospice Movement, within its young, fastdeveloping structure, is established as a Body within the Maltese Community that continues to expand its vision of Palliative Care, Palliative Medicine and Hospice Philosophy by increasing its human, structural and organisational resources. Through the multi-disciplinary team, it reaches out to cancer patients both as a voluntary, charitable organisation but more importantly as a professional one in a wide range of Hospice services.peer-reviewe
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