PRODUCTS OF IDEMPOTENT ENDOMORPHISMS OF RELATIVELY FREE ALGEBRAS WITH WEAK EXCHANGE PROPERTIES
2007 ◽
Vol 50
(2)
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pp. 343-362
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Keyword(s):
AbstractIf $A$ is a stable basis algebra of rank $n$, then the set $S_{n-1}$ of endomorphisms of rank at most $n-1$ is a subsemigroup of the endomorphism monoid of $A$. This paper gives a number of necessary and sufficient conditions for $S_{n-1}$ to be generated by idempotents. These conditions are satisfied by finitely generated free modules over Euclidean domains and by free left $T$-sets of finite rank, where $T$ is cancellative monoid in which every finitely generated left ideal is principal.
1988 ◽
Vol 31
(3)
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pp. 374-379
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2003 ◽
Vol 75
(3)
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pp. 355-384
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Keyword(s):
1979 ◽
Vol 28
(3)
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pp. 335-345
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1971 ◽
Vol 12
(2)
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pp. 187-192
2018 ◽
Vol 17
(02)
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pp. 1850023
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2004 ◽
Vol 03
(02)
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pp. 207-217
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2018 ◽
Vol 154
(5)
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pp. 934-959
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1995 ◽
Vol 38
(4)
◽
pp. 408-411
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2000 ◽
Vol 10
(06)
◽
pp. 739-749
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1981 ◽
Vol 1
(2)
◽
pp. 209-221
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