A note on Möbius functions and a breaking process

2021 ◽  
pp. 2250108
Author(s):  
Emil Daniel Schwab
Keyword(s):  
Inverse Semigroups ◽  
Inverse Monoid ◽  
Interesting Topic ◽  
Monoid Action

Links between Möbius functions and inverse semigroups are an interesting topic for study. In this paper, we restrict our interest to the submonoid of right units (as a Möbius monoid) of a combinatorial bisimple inverse monoid. The Möbius functions at the end of this paper are Möbius functions of broken Möbius categories (broken up into two parts) via a submonoid and a right monoid action.

Inverse semigroup homomorphisms via partial group actions

2001 ◽  
Vol 64 (1) ◽  
pp. 157-168 ◽  
Author(s):  
Benjamin Steinberg
Keyword(s):  
Inverse Semigroup ◽  
Group Actions ◽  
Inverse Semigroups ◽  
Inverse Monoid ◽  
Partial Group ◽  
Inverse Monoids ◽  
Maximal Group ◽  
Special Cases ◽  
Quick Proof ◽  
Group Component

This papar constructs all homomorphisms of inverse semigroups which factor through an E-unitary inverse semigroup; the construction is in terms of a semilattice component and a group component. It is shown that such homomorphisms have a unique factorisation βα with α preserving the maximal group image, β idempotent separating, and the domain I of β E-unitary; moreover, the P-representation of I is explicitly constructed. This theory, in particular, applies whenever the domain or codomain of a homomorphism is E-unitary. Stronger results are obtained for the case of F-inverse monoids.Special cases of our results include the P-theorem and the factorisation theorem for homomorphisms from E-unitary inverse semigroups (via idempotent pure followed by idempotent separating). We also deduce a criterion of McAlister–Reilly for the existence of E-unitary covers over a group, as well as a generalisation to F-inverse covers, allowing a quick proof that every inverse monoid has an F-inverse cover.

scholarly journals Inverse semigroups with certain types of partial automorphism monoids

1990 ◽  
Vol 32 (2) ◽  
pp. 189-195 ◽  
Author(s):  
Simon M. Goberstein
Keyword(s):  
Inverse Semigroup ◽  
General Expression ◽  
Inverse Semigroups ◽  
Inverse Monoid ◽  
Exceptional Groups ◽  
Completely Semisimple

AbstractFor an inverse semigroup S, the set of all isomorphisms betweeninverse subsemigroups of S is an inverse monoid under composition which is denoted by (S) and called the partial automorphism monoid of S. Kirkwood [7] and Libih [8] determined which groups have Clifford partial automorphism monoids. Here we investigate the structure of inverse semigroups whose partial automorphism monoids belong to certain other important classes of inverse semigroups. First of all, we describe (modulo so called “exceptional” groups) all inverse semigroups S such that (S) is completely semisimple. Secondly, for an inverse semigroup S, we find a convenient description of the greatest idempotent-separating congruence on (S), using a well-known general expression for this congruence due to Howie, and describe all those inverse semigroups whose partial automorphism monoids are fundamental.

scholarly journals On a complete topological inverse polycyclic monoid

2016 ◽  
Vol 8 (2) ◽  
pp. 183-194 ◽  
Author(s):  
S.O. Bardyla ◽  
O.V. Gutik
Keyword(s):  
Sufficient Conditions ◽  
Inverse Semigroups ◽  
Infinite Cardinal ◽  
Inverse Monoid ◽  
Inverse Topology

We give sufficient conditions when a topological inverse $\lambda$-polycyclic monoid $P_{\lambda}$ is absolutely $H$-closed in the class of topological inverse semigroups. For every infinite cardinal $\lambda$ we construct the coarsest semigroup inverse topology $\tau_{mi}$ on $P_\lambda$ and give an example of a topological inverse monoid $S$ which contains the polycyclic monoid $P_2$ as a dense discrete subsemigroup.

scholarly journals Inverse semigroups determined by their partial automorphism monoids

2006 ◽  
Vol 81 (2) ◽  
pp. 185-198 ◽  
Author(s):  
Simon M. Goberstein
Keyword(s):  
Inverse Semigroup ◽  
Partial Order ◽  
Inverse Semigroups ◽  
Natural Partial Order ◽  
Inverse Monoid ◽  
Inverse Monoids ◽  
Inverse Subsemigroups

AbstractThe partial automorphism monoid of an inverse semigroup is an inverse monoid consisting of all isomorphisms between its inverse subsemigroups. We prove that a tightly connected fundamental inverse semigroup S with no isolated nontrivial subgroups is lattice determined ‘modulo semilattices’ and if T is an inverse semigroup whose partial automorphism monoid is isomorphic to that of S, then either S and T are isomorphic or they are dually isomorphic chains relative to the natural partial order; a similar result holds if T is any semigroup and the inverse monoids consisting of all isomorphisms between subsemigroups of S and T, respectively, are isomorphic. Moreover, for these results to hold, the conditions that S be tightly connected and have no isolated nontrivial subgroups are essential.

Combinatorially Factorizable Cryptic Inverse Semigroups

2014 ◽  
Vol 57 (3) ◽  
pp. 621-630
Author(s):  
Mario Petrich
Keyword(s):  
Inverse Semigroup ◽  
Inverse Semigroups ◽  
Inverse Monoid ◽  
Direct Products ◽  
Inverse Subsemigroup ◽  
Equality Relation ◽  
Special Case

AbstractAn inverse semigroup S is combinatorially factorizable if S = TG where T is a combinatorial (i.e., 𝓗 is the equality relation) inverse subsemigroup of S and G is a subgroup of S. This concept was introduced and studied byMills, especially in the case when S is cryptic (i.e., 𝓗 is a congruence on S). Her approach is mainly analytical considering subsemigroups of a cryptic inverse semigroup.We start with a combinatorial inverse monoid and a factorizable Clifford monoid and from an action of the former on the latter construct the semigroups in the title. As a special case, we consider semigroups that are direct products of a combinatorial inverse monoid and a group.

Toleransi Religius, Antara Pluralisme dan Pluralitas Agama dalam Perspektif Al-Quran

SUHUF ◽  
2015 ◽  
Vol 6 (1) ◽  
pp. 83-103
Author(s):  
Bagus Purnomo
Keyword(s):  
Religious Freedom ◽  
Original Form ◽  
Basic Difference ◽  
Islamic Perspective ◽  
Interesting Topic ◽  
Religious Doctrine

The emergence of the violence issues concerning religious doctrine is separated from the increasing of the cases of the intolerance in Indonesia. It is for that reason that the discourse about pluralism and plurality of religion becomes the interesting topic. Briefly, the two words above have the same meaning for its similarity in their original form that is “Plural”. However, empirically, those two words have the basic difference then it is added by the word religion in the end of the word (suffix). If the plurality of religion is meant to be the variety of religions, then the meaning of pluralism changes to be the uniformity of religion which eventually arising polemic in Indonesia. Plurality of religion is an unavoidable phenomenon from God.(Sunnatullah). This writing tries to explain how the the Qur’an “speaks” about the tolerance in the plurality of religion and the principles of religious freedom in Islamic perspective.

scholarly journals Physically Based Soap Bubble Synthesis for VR

2021 ◽  
Vol 11 (7) ◽  
pp. 3090
Author(s):  
Sangwook Yoo ◽  
Cheongho Lee ◽  
Seongah Chin
Keyword(s):  
Virtual Reality ◽  
Virtual Space ◽  
Soap Bubble ◽  
Temporal Constraints ◽  
High Expectations ◽  
Soap Bubbles ◽  
Physical Motion ◽  
Head Mounted Display ◽  
Interesting Topic ◽  
Physically Based

To experience a real soap bubble show, materials and tools are required, as are skilled performers who produce the show. However, in a virtual space where spatial and temporal constraints do not exist, bubble art can be performed without real materials and tools to give a sense of immersion. For this, the realistic expression of soap bubbles is an interesting topic for virtual reality (VR). However, the current performance of VR soap bubbles is not satisfying the high expectations of users. Therefore, in this study, we propose a physically based approach for reproducing the shape of the bubble by calculating the measured parameters required for bubble modeling and the physical motion of bubbles. In addition, we applied the change in the flow of the surface of the soap bubble measured in practice to the VR rendering. To improve users’ VR experience, we propose that they should experience a bubble show in a VR HMD (Head Mounted Display) environment.

scholarly journals Inverse semigroups with idempotent-fixing automorphisms

2014 ◽  
Vol 89 (2) ◽  
pp. 469-474 ◽  
Author(s):  
João Araújo ◽  
Michael Kinyon
Keyword(s):  
Inverse Semigroups

scholarly journals Implicit Interpretation of Indonesian Export Bans on LME Nickel Prices: Evidence from the Announcement Effect

Risks ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 93
Author(s):  
Byungkwon Lim ◽  
Hyeon Sook Kim ◽  
Jaehwan Park
Keyword(s):  
Metal Exchange ◽  
London Metal Exchange ◽  
Announcement Effect ◽  
Knowledge Gaps ◽  
Indonesian Government ◽  
Interesting Topic ◽  
The Impact

Forecasting of LME (London Metal Exchange) nickel prices remains an interesting topic but lacks consensus. This study aims to fill knowledge gaps by demonstrating the announcement effect of export bans by the Indonesian government. This article focuses on Indonesia because Indonesia produces more than 60% of global nickel ore. We identified the sequence of two episodes in which Indonesian export bans of nickel ore appeared to increase LME nickel prices through the Romer and Romer (1989) approach. The impact of the Indonesian export ban in 2014 is somewhat larger than that of 2019. The shock on the LME nickel market in 2014 was sustained for a while after the ban was implemented. We believe that this is the first export ban that has had unexpected effects within the market.

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