A Characterization of Adequate Semigroups by Forbidden Subsemigroups

نویسندگان

  • JOÃO ARAÚJO
  • MICHAEL KINYON
چکیده

A semigroup is amiable if there is exactly one idempotent in each R⇤-class and in each L⇤-class. A semigroup is adequate if it is amiable and if its idempotents commute. We characterize adequate semigroups by showing that they are precisely those amiable semigroups which do not contain isomorphic copies of two particular nonadequate semigroups as subsemigroups.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On semigroups with lower semimodular lattice of subsemigroups

The question of which semigroups have lower semimodular lattice of subsemigroups has been open since the early 1960’s, when the corresponding question was answered for modularity and for upper semimodularity. We provide a characterization of such semigroups in the language of principal factors. Since it is easily seen (and has long been known) that semigroups for which Green’s relation J is tri...

متن کامل

Automatic structures for subsemigroups of Baumslag–Solitar semigroups

This paper studies automatic structures for subsemigroups of Baumslag–Solitar semigroups (that is, semigroups presented by ⟨x, y | (yx, xy)⟩ where m,n ∈ N). A geometric argument (a rarity in the field of automatic semigroups) is used to show that if m > n, all of the finitely generated subsemigroups of this semigroup are [right-] automatic. If m < n, all of its finitely generated subsemigroups ...

متن کامل

On the lattice of full eventually regular subsemigroups

We generalize to eventually regular (or ‘π-regular’) semigroups the study of the lattice of full regular subsemigroups of a regular semigroup, which has its most complete exposition in the case of inverse semigroups. By means of a judicious definition, it is shown that the full eventually regular subsemigroups of such a semigroup form a complete lattice LF , which projects onto the lattices of ...

متن کامل

The Lattices of Group Fuzzy Congruences and Normal Fuzzy Subsemigroups on E-Inversive Semigroups

The aim of this paper is to investigate the lattices of group fuzzy congruences and normal fuzzy subsemigroups on E-inversive semigroups. We prove that group fuzzy congruences and normal fuzzy subsemigroups determined each other in E-inversive semigroups. Moreover, we show that the set of group t-fuzzy congruences and the set of normal subsemigroups with tip t in a given E-inversive semigroup f...

متن کامل

On classification of maximal nilpotent subsemigroups

We develop a general approach to the study of maximal nilpotent subsemigroups of finite semigroups. This approach can be used to recover many known classifications of maximal nilpotent subsemigroups, in particular, for the symmetric inverse semigroup, the symmetric semigroup, and the factor power of the symmetric group. We also apply this approach to obtain a classification of maximal nilpotent...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2011