On automorphisms of monotone transformation posemigroups

2021 ◽  
pp. 2250032
Author(s):  
Dilawar Juneed Mir ◽  
Aftab Hussain Shah ◽  
Shabir Ahmad Ahanger
Keyword(s):  
Partial Transformation ◽  
Monotone Transformation ◽  
Full Transformation ◽  
Simple Generalization

In this paper, we provide a simple generalization of results of Sullivan for [Formula: see text] the full transformation monotone pomonoid and for [Formula: see text] the partial transformation monotone pomonoid by showing that every automorphism of [Formula: see text] and [Formula: see text] is inner induced by the elements of [Formula: see text] the pogroup of all ordered bijections on [Formula: see text]. We also show that [Formula: see text] is isomorphic to [Formula: see text]. Finally, we apply these results to get some more results in this direction.

scholarly journals Automorphisms of normal partial transformation semigroups

1987 ◽  
Vol 29 (2) ◽  
pp. 149-157 ◽  
Author(s):  
Inessa Levi
Keyword(s):  
Symmetric Group ◽  
Transformation Semigroup ◽  
Partial Transformation ◽  
Transformation Semigroups ◽  
Full Transformation ◽  
Full Transformation Semigroup ◽  
Infinite Set

We let X be an arbitrary infinite set. A semigroup S of total or partial transformations of X is called -normal if hSh-1 = S, for all h in , the symmetric group on X. For example, the full transformation semigroup , the semigroup of all partial transformations , the semigroup of all 1–1 partial transformations and all ideals of and are -normal.

scholarly journals Skew Pairs of Idempotents in Partial Transformation Semigroups

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 2
Author(s):  
Panuwat Luangchaisri ◽  
Thawhat Changphas
Keyword(s):  
Regular Semigroup ◽  
Transformation Semigroup ◽  
Acta Math ◽  
Partial Transformation ◽  
Transformation Semigroups ◽  
Full Transformation ◽  
Full Transformation Semigroup ◽  
Left Regular

Let S be a regular semigroup. A pair (e,f) of idempotents of S is said to be a skew pair of idempotents if fe is idempotent, but ef is not. T. S. Blyth and M. H. Almeida (T. S. Blyth and M. H. Almeida, skew pair of idempotents in transformation semigroups, Acta Math. Sin. (English Series), 22 (2006), 1705–1714) gave a characterization of four types of skew pairs—those that are strong, left regular, right regular, and discrete—existing in a full transformation semigroup T(X). In this paper, we do in this line for partial transformation semigroups.

scholarly journals Generalised partial transformation semigroups

1975 ◽  
Vol 19 (4) ◽  
pp. 470-473 ◽  
Author(s):  
R. P. Sullivan
Keyword(s):  
Partial Transformation ◽  
Transformation Semigroups ◽  
Full Transformation ◽  
Special Case

It is well-known that for any set X, px, the semigroup of all partial transformations on X, can be embedded in Jx∪a for some a ∉ X (see for example Clifford and Preston (1967) and Ljapin (1963)). Recently Magill (1967) has considered a special case of what we call ‘generalised partial transformation semigroups’. We show here that any such semigroup can always be embedded in a full transformation smigroup in which the operation is not in general equal to the usual composition of mappinas. We then examine conditions under which such a semigroup, (J x, θ), is isomorphic to the semigroup, under composition, of all transformations on the same set X.

Mortal Democracy and Plato’s Apology

2020 ◽  
pp. 009059172098295
Author(s):  
Elizabeth Barringer
Keyword(s):  
Democratic Politics ◽  
Political Life ◽  
Partial Transformation ◽  
Critical Space ◽  
Athenian Democracy ◽  
Precarious Work ◽  
Democratic Practice

The Apology is often read as showing a conflict between democracy and philosophy. I argue here that Socrates’s defense critically engages deeply political Athenian conventions of death, showing a mutual entanglement between Socratic philosophy and democratic practice. I suggest that Socrates’s aporetic insistence within the Apology that we “do not know if death is a good or a bad thing” structures a critical space of inquiry that I term “mortal ignorance;” a space from which Socrates reapproaches settled questions of death’s appropriate place in political life, ultimately prompting a partial transformation of Athenian democracy. I argue here that Socratic mortal ignorance supports a self-reflective politics of death, one which produces many potential responses and accepts the impossibility of closing off death’s meaning in any final sense—an aporia suitable for the unending, precarious work of democratic politics.

scholarly journals Nonrandom cytogenetic changes accompany malignant progression in clonal lines abelson virus-infected lymphocytes

Blood ◽  
1994 ◽  
Vol 84 (12) ◽  
pp. 4301-4309 ◽  
Author(s):  
SS Clark ◽  
Y Liang ◽  
CK Reedstrom ◽  
SQ Wu
Keyword(s):  
Tumor Progression ◽  
Murine Leukemia Virus ◽  
Leukemia Virus ◽  
Lymphoid Cells ◽  
Full Transformation ◽  
Cytogenetic Abnormalities ◽  
Cytogenetic Changes ◽  
Abelson Murine Leukemia Virus ◽  
Murine Leukemia ◽  
Over Time

Initially, lymphoid cells transformed by v-abl or BCR/ABL oncogenes are poorly oncogenic but progress to full transformation over time. Although expression of the oncogene is necessary to initiate and maintain transformation, other molecular mechanisms are thought to be required for full transformation. To determine whether tumor progression in ABL oncogene-transformed lymphoid cells has a genetic basis, we examined whether progression of the malignant phenotype of transformed clones correlates with particular cytogenetic abnormalities. A modified in vitro bone marrow transformation model was used to obtain clonal Abelson murine leukemia virus-transformed B lymphoid cells that were poorly oncogenic. Multiple subclones were then derived from each clone and maintained over a marrow-derived stromal cell line for several weeks. Over time, clonally related Abelson murine leukemia virus-transformed subclones progressed asynchronously to full transformation. The data show that tumor progression can occur in the absence of detectable cytogenetic changes but, more importantly, that certain cytogenetic abnormalities appear reproducibly in highly malignant subclones. Therefore, three independent subclones showed deletion in a common region of chromosome 13. Other highly malignant cells carried a common breakpoint in the X chromosome, and, finally, two subclones carried an additional chromosome 5. These results are consistent with the hypothesis that ABL oncogenes are sufficient for the initial transformation of cells but that additional genetic events can drive oncogenic progression. These observations further suggest that diverse genetic mechanisms may be able to drive tumor progression in cells transformed with ABL oncogenes.

scholarly journals Products of two idempotent transformations over arbitrary sets and vector spaces

1998 ◽  
Vol 57 (1) ◽  
pp. 59-71 ◽  
Author(s):  
Rachel Thomas
Keyword(s):  
Vector Space ◽  
Transformation Semigroup ◽  
Vector Spaces ◽  
Endomorphism Monoid ◽  
Linear Transformations ◽  
Arbitrary Vector ◽  
Full Transformation ◽  
Full Transformation Semigroup

In this paper we consider the characterisation of those elements of a transformation semigroup S which are a product of two proper idempotents. We give a characterisation where S is the endomorphism monoid of a strong independence algebra A, and apply this to the cases where A is an arbitrary set and where A is an arbitrary vector space. The results emphasise the analogy between the idempotent generated subsemigroups of the full transformation semigroup of a set and of the semigroup of linear transformations from a vector space to itself.

scholarly journals Nilpotents in semigroups of partial transformations

1997 ◽  
Vol 55 (3) ◽  
pp. 453-467 ◽  
Author(s):  
R. P. Sullivan
Keyword(s):  
Partial Transformation ◽  
Index 2 ◽  
Infinite Set

In 1987, Sullivan determined when a partial transformation α of an infinite set X can be written as a product of nilpotent transformations of the same set: he showed that when this is possible and the cardinal of X is regular then α is a product of 3 or fewer nilpotents with index at most 3. Here, we show that 3 is best possible on both counts, consider the corresponding question when the cardinal of X is singular, and investigate the role of nilpotents with index 2. We also prove that the nilpotent-generated semigroup is idempotent-generated but not conversely.

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