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On graph products of automatic monoids

A. Veloso Da Costa (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The graph product is an operator mixing direct and free products. It is already known that free products and direct products of automatic monoids are automatic. The main aim of this paper is to prove that graph products of automatic monoids of finite geometric type are still automatic. A similar result for prefix-automatic monoids is established.

On graph products of automatic monoids

A. Veloso da Costa (2010)

RAIRO - Theoretical Informatics and Applications

The graph product is an operator mixing direct and free products. It is already known that free products and direct products of automatic monoids are automatic. The main aim of this paper is to prove that graph products of automatic monoids of finite geometric type are still automatic. A similar result for prefix-automatic monoids is established.

On homological classification of pomonoids by GP-po-flatness ofS-posets

Xingliang Liang, Xinyang Feng, Yanfeng Luo (2016)

Open Mathematics

In this paper, we introduce GP-po-flatness property of S-posets over a pomonoid S, which lies strictly between principal weak po-flatness and po-torsion freeness. Furthermore, we investigate the homological classification problems of pomonoids by using this new property. Finally, we consider direct products of GP-po-flat S-posets. As an application, characterizations of pomonoids over which direct products of nonempty families of principally weakly po-flat S-posets are principally weakly po-flat...

On homological classification of pomonoids by regular weak injectivity properties of S-posets

Xia Zhang, Valdis Laan (2007)

Open Mathematics

If S is a partially ordered monoid then a right S-poset is a poset A on which S acts from the right in such a way that the action is compatible both with the order of S and A. By regular weak injectivity properties we mean injectivity properties with respect to all regular monomorphisms (not all monomorphisms) from different types of right ideals of S to S. We give an alternative description of such properties which uses systems of equations. Using these properties we prove several so-called homological...

On ideals in regular ternary semigroups

Tapan K. Dutta, Sukhendu Kar, Bimal K. Maity (2008)

Discussiones Mathematicae - General Algebra and Applications

In this paper we study some interesting properties of regular ternary semigroups, completely regular ternary semigroups, intra-regular ternary semigroups and characterize them by using various ideals of ternary semigroups.

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