Variants of the 3𝑁+1 conjecture and multiplicative semigroups

2005 ◽  
pp. 121-127 ◽  
Author(s):  
Hershel M. Farkas
Keyword(s):  
Multiplicative Semigroups

Question of the mixed product of dependent multiplicative semigroups

1987 ◽  
Vol 39 (2) ◽  
pp. 134-139 ◽  
Author(s):  
T. V. Karataeva ◽  
T. A. Skorokhod
Keyword(s):  
Mixed Product ◽  
Multiplicative Semigroups

Fragmented rings

1978 ◽  
Vol 78 (3-4) ◽  
pp. 273-283 ◽  
Author(s):  
Paul Dubreil
Keyword(s):  
Subsequent Paper ◽  
Multiplicative Semigroup ◽  
Finite Set ◽  
Multiplicative Semigroups

SynopsisThe publication of the results in this paper has been delayed, for non-mathematical reasons. However, the author has given lectures on these results in Smolenice [2], Gainesville, Tulane. Riverside (1971), Milan (1972) and in Paris. The main consideration in this paper is the notion of a fragmented ring and its multiplicative semigroup. A fragmented ring is a ring with an identity having a finite set of idempotents, these commuting and therefore being central. In a subsequent paper we shall consider associated ideas in a purely semigroup-theoretic context and, in so doing, point out some differences between general semigroups and those semigroups that are the multiplicative semigroups of rings.

scholarly journals Abundant Rees matrix semigroups

1987 ◽  
Vol 42 (1) ◽  
pp. 132-142 ◽  
Author(s):  
M. V. Lawson
Keyword(s):  
Regular Semigroups ◽  
Rees Matrix Semigroups ◽  
Abundant Semigroups ◽  
Multiplicative Semigroups ◽  
Matrix Semigroups ◽  
Cancellative Monoids

AbstractThe class of abundant semigroups originally arose from ‘homological’ considerations in the theory of S-systems: they are the semigroup theoretic counterparts of PP-rings. Cancellative monoids, full subsemigroups of regular semigroups as well as the multiplicative semigroups of PP-rings are abundant. In this paper we investigate the properties of Rees matrix semigroups over abundant semigroups. Some of our results generalise McAlister's work on regular Rees matrix semigroups.

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