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On strongly ( P ) -cyclic acts

Akbar Golchin, Parisa Rezaei, Hossein Mohammadzadeh (2009)

Czechoslovak Mathematical Journal

By a regular act we mean an act such that all its cyclic subacts are projective. In this paper we introduce strong ( P ) -cyclic property of acts over monoids which is an extension of regularity and give a classification of monoids by this property of their right (Rees factor) acts.

On structure space of Γ -semigroups

S. Chattopadhyay, S. Kar (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we introduce the notion of the structure space of Γ -semigroups formed by the class of uniformly strongly prime ideals. We also study separation axioms and compactness property in this structure space.

On super hamiltonian semigroups

Kar-Ping Shum, X. M. Ren (2004)

Czechoslovak Mathematical Journal

The concept of super hamiltonian semigroup is introduced. As a result, the structure theorems obtained by A. Cherubini and A. Varisco on quasi commutative semigroups and quasi hamiltonian semigroups respectively are extended to super hamiltonian semigroups.

On the arithmetic of arithmetical congruence monoids

M. Banister, J. Chaika, S. T. Chapman, W. Meyerson (2007)

Colloquium Mathematicae

Let ℕ represent the positive integers and ℕ₀ the non-negative integers. If b ∈ ℕ and Γ is a multiplicatively closed subset of b = / b , then the set H Γ = x | x + b Γ 1 is a multiplicative submonoid of ℕ known as a congruence monoid. An arithmetical congruence monoid (or ACM) is a congruence monoid where Γ = ā consists of a single element. If H Γ is an ACM, then we represent it with the notation M(a,b) = (a + bℕ₀) ∪ 1, where a, b ∈ ℕ and a² ≡ a (mod b). A classical 1954 result of James and Niven implies that the only ACM...

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