Pure -bands

Karin Cvetko-Vah

doi:10.1007/s00233-004-0177-2

Pure -bands

Karin Cvetko-Vah

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Jonathan Leech proved in [8] that the multiplicative reduct of a skew lattice in a ring is always a regular band. A band that is closed under the operation is called a -band. A -band is also always regular. We show that a regular band does not generate a -band in general but does so in the special case of regular pure bands. An exact condition for a pure -band to form a skew lattice was found in [1].

Original language	English
Pages (from-to)	93-101
Number of pages	9
Journal	Semigroup Forum
Volume	71
Issue number	1
DOIs	https://doi.org/10.1007/s00233-004-0177-2
Publication status	Published - 1 Sept 2006

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title = "Pure -bands",

abstract = "Jonathan Leech proved in [8] that the multiplicative reduct of a skew lattice in a ring is always a regular band. A band that is closed under the operation is called a -band. A -band is also always regular. We show that a regular band does not generate a -band in general but does so in the special case of regular pure bands. An exact condition for a pure -band to form a skew lattice was found in [1].",

author = "Karin Cvetko-Vah",

year = "2006",

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doi = "10.1007/s00233-004-0177-2",

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AU - Cvetko-Vah, Karin

PY - 2006/9/1

Y1 - 2006/9/1

N2 - Jonathan Leech proved in [8] that the multiplicative reduct of a skew lattice in a ring is always a regular band. A band that is closed under the operation is called a -band. A -band is also always regular. We show that a regular band does not generate a -band in general but does so in the special case of regular pure bands. An exact condition for a pure -band to form a skew lattice was found in [1].

AB - Jonathan Leech proved in [8] that the multiplicative reduct of a skew lattice in a ring is always a regular band. A band that is closed under the operation is called a -band. A -band is also always regular. We show that a regular band does not generate a -band in general but does so in the special case of regular pure bands. An exact condition for a pure -band to form a skew lattice was found in [1].

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U2 - 10.1007/s00233-004-0177-2

DO - 10.1007/s00233-004-0177-2

M3 - Article

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SN - 0037-1912

VL - 71

SP - 93

EP - 101

JO - Semigroup Forum

JF - Semigroup Forum

IS - 1

ER -

Pure -bands

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